
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 $O$. The larger square has sides of length $2$, and the smaller square has sides of length $1$. The line $\overline{AB}$, which is a segment between the larger and smaller squares and one which lies along their shared diagonal path, has a length of $\frac{3}{4}$. Calculate the area of the octagon $ABCDEFGH$ formed by the intersecting points of the squares' sides, given that the smaller square is rotated $45^\circ$ with respect to the larger one. Express the area as a fraction $m/n$, where $m$ and $n$ are relatively prime integers, and find $m+n$.

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