
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
In a square with a side length of \(a\), the midpoints of two adjacent sides are connected to each other and to the opposite vertex of the square. Determine the area of the inner triangle.

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