
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 concentric squares share the same center $O$, where the side length of the smaller square is 2 and the larger square has a side length of 3. The length of $\overline{AB}$ is $1/4$, and the area of the octagon $ABCDEFGH$ formed by the lines connecting alternate vertices of the larger square to the nearer edges of the smaller square is $m/n$, 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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