Use value retrieved from getFieldValue as argument to apex call in LWC

Question

What I am looking to achieve is for a component on a Lightning record page to take the ID of the record in context, get the value of a field upon that record, then feed that into an Apex method to return a list of records to display within that component.

Let's say that I have some object that has a lookup to Account. What I want to do is have a Lightning record page for that object that will show me the Contacts for the Account in that lookup field.

My efforts so far have not produced positive results. Here's a flavour of what I have:

Apex

@AuraEnabled(cacheable=true)
public static List<Contact> getContacts(Id accountId) {
    return [SELECT Id FROM Contact WHERE AccountId = :accountId]; 
}

LWC Javascript

import { LightningElement, api, wire, track } from 'lwc';
import { getRecord, getFieldValue } from 'lightning/uiRecordApi';
import getContacts from '@salesforce/apex/Contacts.getContacts';
import ACCOUNT_ID from '@salesforce/schema/CustomObject__c.Account__c';

export default class ShowContacts extends LightningElement {
    @track foundContacts;
    @api recordId;

    @wire(getRecord, { recordId: '$recordId', fields: [ ACCOUNT_ID ] })
    account;

    @wire(getContacts, { accountId: this.accountId() })
    contacts({ error, data }) {
        if (data) {
            this.foundContacts = data;
            this.error = undefined;
        }
        else {
            this.error = error;
            this.foundContacts = undefined;
        }
    }

    get accountId() {
        return getFieldValue(this.account.data, ACCOUNT_ID);
    }
}

UPDATE:

I managed to get around this by removing the whole concept of getting the Account ID within the component, and doing that step within the Apex class at the expense of 1 more SOQL query, but it would be great if I could achieve that all within the component.

Is it impossible to retrieve a value from a referenced record and pass that into an Apex call in Lightning Web Components?