
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 exist constants \(b_1, b_2, b_3, b_4, b_5\) such that
\[
\sin^5 \theta = b_1 \sin \theta + b_2 \sin 2 \theta + b_3 \sin 3 \theta + b_4 \sin 4 \theta + b_5 \sin 5 \theta
\]
for all angles \(\theta\). Find \(b_1^2 + b_2^2 + b_3^2 + b_4^2 + b_5^2\).

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