
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
If $b > 1$, $\sin x > 0$, $\cos x > 0$, and $\log_b (\sin^2 x) = a$, find $\log_b (\cos^2 x)$.
A) $\log_b (1 - b^{a/2})$
B) $\sqrt{1-a^2}$
C) $b^{a^2}$
D) $\log_b (1 - b^a)$
E) $\text{none of these}$

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