
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
Square $ABCD$ is inscribed in a circle. Square $IJKL$ has vertices $I$ and $J$ on $\overline{CD}$ and vertices $K$ and $L$ on the circle. If the area of square $ABCD$ is $4$, then the area of square $IJKL$ can be expressed as $\frac {p}{q}$, where $p$ and $q$ are relatively prime positive integers and $p < q$. Find $10q + p$.

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