
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
Two squares with the same center \(O\) and side lengths of 2 are shown. The length of \(\overline{AB}\) is \(\frac{50}{121}\). Find the area of the resulting octagon \(ABCDEFGH\), represented as a fraction \(m/n\), where \(m\) and \(n\) are coprime integers. Calculate \(m+n\).

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