
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 two squares shown share the same center \( O \) and have sides of length 1. The length of \( \overline{AB} \) is \( \frac{17}{40} \) and the area of octagon \( ABCDEFGH \) is \( \frac{m}{n}, \) where \( m \) and \( n \) are relatively prime positive integers. Find \( m+n. \)

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