
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 \(\cos ^{4} \theta + \sin ^{4} \theta + (\cos \theta \cdot \sin \theta)^{4} + \frac{1}{\cos ^{4} \theta + \sin ^{4} \theta} = \frac{41}{16}\), find the value of \(\sin ^{2} \theta\).

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