[Laravel5/FB] Post links to my Facebook page as the page itself

[Alhazred]

I've got a website where users can fill a form, the web application stores the data into the database.
Those data are used to create contents on the site.
As a user submits the form, I want to post a link to the Facebook page related to the website, but not in name of the user, but as the page itself.
I've read a lot of tutorials around, but I couldn't have this working.
This is my code at the moment, but of course it doesn't work

FacebookSession::setDefaultApplication($app_id, $app_secret);

$session = FacebookSession::newAppSession();

try {
    $session->validate();
} catch (FacebookRequestException $ex) {
    echo $ex->getMessage();
} catch (\Exception $ex) {
    echo $ex->getMessage();
}

if($session)
{
    try {
        $response = (new FacebookRequest(
            $session, 'POST', '/me/feed', array(
                'link' => 'www.mysite.it',
                'message' => 'some text'
            )
        ))->execute()->getGraphObject();
        echo "Posted with id: " . $response->getProperty('id');
    } catch(FacebookRequestException $e) {
        echo "Exception occured, code: " . $e->getCode() . 
             " with message: " . $e->getMessage();
    }
} 

What I get is this error message:

"Exception occured, code: 2500 with message: An active access token must be used to query information about the current user."

As I've understood I miss to login as the page, but I can't uderstand how to do so.
Could any one tell me how to chenge the code?