If X and Y are the inputs, the given circuit works as _______.

The circuit consists of four NAND gates.

The first two NAND gates have their inputs tied together, acting as NOT gates. Their outputs are $\overline{X}$ and $\overline{Y}$.

These outputs are fed into the third NAND gate. The output of this gate is:
$y' = \overline{\overline{X} \cdot \overline{Y}}$

Using De Morgan's theorem:
$y' = \overline{\overline{X}} + \overline{\overline{Y}} = X + Y$

This output is fed into the fourth NAND gate, which also has its inputs tied together, acting as a NOT gate. The final output is:
Output $= \overline{X + Y}$

This represents the Boolean expression for a NOR gate.

Answer: NOR gate