
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 base of a triangle is \( a \), and its height is \( m \). Draw a square on the base of the triangle such that two of its vertices lie on the sides of the triangle. Subsequently, inscribe a square in the resulting smaller triangle in the same manner, and continue this process indefinitely. What is the sum of the areas of all the squares?

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