How to get dropdown select value session in another page in Laravel 8

I wish I had a few options in one form. The user will select the report type from this form, and according to that selected value, I want to show the input field in a different form. I have been trying to do this for two days but I can't do it. It would be very helpful if someone could help

This is my form one code

<form action="{{url('prepare/create/report')}}" method="post">
<label for="">Report Type</label>
<select name="report_type">
@foreach($report_type as $data)
<option value="{{$data->id}}">{{$data->name}}</option>
@endforeach
</select>
</form>

I want to get the above form dropdown value session data in this form

<form action="{{url('start/create/report')}}" method="post">
@csrf
@if($report->report_type == '1001')
<label for="">Student Name</label>
<input type="text" name="name" value="">
@else
<label for="">Teacher Name</label>
<input type="text" name="name" value="">
@endif
</form>

I'm new to Laravel and don't really understand the season so I don't understand how my controller code will be.

This is my route code

Route::get('/prepare/create/report', [AdminController::class, 'PrepareCreateReport']);
Route::post('/prepare/create/report', [AdminController::class, 'StoreCreateReport']);
Route::get('/create/report/start', [AdminController::class, 'StartReportCreation'])->name('create.report');