
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
Let \(a\), \(b\), and \(c\) be angles in a triangle such that:
\begin{align*}
\sin a &= \cos b, \\
\sin b &= \cos c, \\
\sin c &= \cos a.
\end{align*}
Find the value of \(\cos^2 a + \sin^2 b.\)

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