Solidity: Functions that require a return value it doesn't return anything but still work

I was reading some functions of UniswapV2Router and I face the following code:

function swapExactETHForTokens(uint amountOutMin, address[] calldata path, address to, uint deadline)
        external
        virtual
        override
        payable
        ensure(deadline)
        returns (uint[] memory amounts)
    {
        require(path[0] == WETH, 'UniswapV2Router: INVALID_PATH');
        amounts = UniswapV2Library.getAmountsOut(factory, msg.value, path);
        require(amounts[amounts.length - 1] >= amountOutMin, 'UniswapV2Router: INSUFFICIENT_OUTPUT_AMOUNT');
        IWETH(WETH).deposit{value: amounts[0]}();
        assert(IWETH(WETH).transfer(UniswapV2Library.pairFor(factory, path[0], path[1]), amounts[0]));
        _swap(amounts, path, to);
    }

The function return uint[] memory amounts but actually there is no return in the body. Can you explain me what I miss?

I was expecting to see this variable declared somewhere but I still didn't see it anywhere.

returns (uint[] memory amounts)

This snippet declares the amounts variable and states that the amounts variable should be returned at the end of the function.

amounts = UniswapV2Library.getAmountsOut(factory, msg.value, path);

And this line assigns a value to amounts.

It's simply a shorthand syntax for returning specific variables at the end of the function without having to explicitly write the return statement.

Another example:

function foo() external pure returns (uint256 number) {
    number = 100;
    // TODO rest of your function
}

returns the same value as

function foo() external pure returns (uint256) {
    uint256 number = 100;
    // TODO rest of your function
    return number;
}

From the docs page:

The names of return variables can be omitted. Return variables can be used as any other local variable and they are initialized with their default value and have that value until they are (re-)assigned.

You can either explicitly assign to return variables and then leave the function as above, or you can provide return values (either a single or multiple ones) directly with the return statement: