
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
Define \( f_n(x) = \sin^n x + \cos^n x \). Determine for how many \( x \) in the interval \([0, 2\pi]\) the equation
\[8f_4(x) - 6f_6(x) = 4f_2(x)\]
is true.
A) 0
B) 2
C) 4
D) 6
E) 8

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