
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
A square and a rectangle are inscribed in a circle and share a vertex. One of the angles at the shared vertex in the rectangle is $135^\circ$. The square and rectangle only intersect at this vertex. If $ABC$ is a triangle where $AB$ and $BC$ are sides of the square and rectangle respectively, and $ABC$ is isosceles with $AB=BC$, find the measure of angle $BAC$.

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