
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
Let \( g_n (x) = \text{sin}^n x + \text{cos}^n x. \) For how many \( x \) in \([0, 2\pi]\) is it true that
\[ 10g_{8}(x) - 6g_{10}(x) = 2g_{2}(x)? \]
A) 0
B) 2
C) 4
D) 8 
E) More than 8

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