
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
Given \( x \in [0, 2\pi] \), determine the maximum value of the function 
\[ 
f(x) = \sqrt{4 \cos^2 x + 4 \sqrt{6} \cos x + 6} + \sqrt{4 \cos^2 x - 8 \sqrt{6} \cos x + 4 \sqrt{2} \sin x + 22}.
\]

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