I am new to salesforce and still under training so i need some help to check if account exists or not. Here is the code that i have written so far.

Following is my visualforce page

<apex:page controller="AddAccountController" tabStyle="Account" standardStylesheets="false" showHeader="false" sidebar="false">
    <style>
        .myFormStyle {
        background-color: #D3D3D3;
        }
        .tableBorder
        {
        
        border:3px outset black;
        }
        .innerTableBorder{
        border-top:2px dotted black;
        border-left:2px dotted black;
        }
        function myFunction() {
        var x = document.getElementById("fname");
        x.value = x.value.toUpperCase();
        }
    </style>
    
    
    
    <apex:form styleClass="myFormStyle">
        <div>
            <apex:pageBlock title="Add Account">
                <apex:pageBlockButtons location="top" >                   
                    <apex:commandButton value="Save" action="{!save}" reRender="accountList"  />
                    <apex:commandButton value="Cancel" action="{!cancel}" />
                </apex:pageBlockButtons>  
                <apex:pageBlockSection title="Account Details" columns="1">            
                    <apex:inputField id="accountName" value="{!act.name}"/> 
                    <apex:inputField value="{!act.site}"/> 
                    <apex:inputField value="{!act.type}"/> 
                    <apex:inputField value="{!act.accountNumber}"/>              
                </apex:pageBlockSection>         
            <apex:pageBlockTable value="{!Account}" var="acc" id="accountList" styleClass="tableBorder">              
                <apex:column value="{!acc.Name}" styleClass="innerTableBorder" />            
                <apex:column value="{!acc.Site}" styleClass="innerTableBorder" />               
                <apex:column value="{!acc.type}" styleClass="innerTableBorder" />               
            </apex:pageBlockTable>
        </apex:pageBlock>
    </div>
</apex:form>
</apex:page>

Here on its my controller
 

public class AddAccountController {
    
    public List <Account> account=new List <Account>();
    public Account act{get;set;}
    
    public AddAccountController() {       
        act = new Account();
    }
    
    public List <Account> getAccount() {
        account = [SELECT Id, Name, Site, Type FROM Account order by createddate desc limit 20];
        return account;
    }
    
    public PageReference cancel() {
        return null;
    }
    
    public PageReference save() {
        system.debug('act name:' + act.name + ' = ' + act.accountNumber);
        upsert act;
        return null;
    }
    public Account checkAccount(){
        String accountName =System.currentPageReference().getParameters().get('accountName');
        account = [SELECT Id, Name, Site, Type FROM Account WHERE Name = accountName];
        return act;
    }
}

I am trying to get an icon next to account name field if it exists. Right now my plan is to check if the account exists in the Account array list. if it does then i would like to show a cross next to account field and if it does not exist then a tick next to the account field. Help would be appreciated.