
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A square $ABCD$ is inscribed in a circle. A second square $JKLM$ has vertices $J$ and $K$ on $\overline{CD}$ and vertices $L$ and $M$ on the circle, similar to square $EFGH$ in the original problem. A third square $PQRS$ is inscribed such that vertices $P$ and $Q$ lie on $\overline{AD}$ and vertices $R$ and $S$ lie on the circle. If the area of square $ABCD$ is 4, find the area of square $PQRS$.

Present the answer in LaTex format: \boxed{Your answer}
user