
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 triangle $ABC$, $\angle ABC = \angle BCA = 45^\circ$, and $\overline{BC} = 2$. A circle with center $O$ and radius $r$ is inscribed in $\triangle ABC$, tangent to sides $\overline{AB}$, $\overline{BC}$, and $\overline{CA}$ at points $P$, $Q$, and $R$ respectively. Find the fraction of the area of $\triangle ABC$ that lies outside the circle.
A) $\frac{12 - 8\sqrt{2}}{49}$
   B) $\frac{7 - 4\sqrt{2}}{49}$
   C) $1 - \frac{14\pi}{49}$
   D) $1 - \frac{2\pi(7 - 4\sqrt{2})}{49}$ 
   E) $\frac{1}{2}$

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