
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
Given a square with a side length of \( a \), determine the sides of an isosceles triangle of equal area, where the sum of the lengths of its base and the altitude dropped to it equals the sum of the lengths of the two equal sides.

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