
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
Consider a large square with a side length of 12 inches and a smaller square with a side length of 5 inches placed such that one of its corners touches a corner of the larger square, and one side is parallel to and completely touching one side of the larger square. Calculate the area of the shaded region which is formed by a triangle within the smaller square, as in the setup described. The triangle is formed by extending a diagonal of the smaller square until it meets the opposite side of the larger square.

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