
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
There are constants $b_1$, $b_2$, $b_3$ such that
\[\cos^3 \theta = b_1 \cos \theta + b_2 \cos 2 \theta + b_3 \cos 3 \theta\]
for all angles $\theta$. Find \(b_1^2 + b_2^2 + b_3^2\).

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