
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 that f(x) = 12sin(x + π/6)cosx - 3, x ∈ [0, π/4].
(1) Find the maximum and minimum values of f(x);
(2) CD is the angle bisector of △ABC, where AC = f(x)<sub>max</sub>, BC = f(x)<sub>min</sub>, and CD = 2√2. Find ∠C.

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