
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
The shaded quadrilateral is a rectangle with one base being the side of a square and the other base being the diagonal of another square. Let's denote the side length of the smaller square as \(x\). Then, the side length of the larger square is \(\sqrt{10}x\), because of the information displayed in the diagram.

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