
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
Find the range of the function \( f(x)=\sqrt{36-g^2(x)} \), where \( g(x) = -8 - 2 \cos 8x - 4 \cos 4x \).

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