
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 the rectangle \(ABCD\), point \(F\) is the midpoint of side \(BC\) and point \(H\) is the trisection point of side \(CD\) closer to \(C\). What is the maximum possible measure of angle \(HAF\)?

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