refresh svelte select component after adding an option

I am trying to make a select component update itself after adding an option but I can't. Here is my code:

<script>  const options = ['first_option']  const addEventSignal = () => {    const option = prompt('Please enter new option', '')    if (option) {      options.push(option)    }  }  const doSomething = event => {    console.log(event)  }</script><style></style><div><select bind:value={options} on:change={doSomething}>    {#if options}      {#each options as option}<option value={option}>{option}</option>      {/each}    {/if}</select><button type="button" on:click={addEventSignal}>Add Signal</button></div>

If I reload the component it shows the new option but I would like to have the new option in the select list as soon as the input dialog is gone.