
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
In triangle \( \triangle ABC \), it is known that \( AC=3 \) and the three interior angles \( A \), \( B \), and \( C \) form an arithmetic sequence.  
(1) If \( \cos C= \frac {\sqrt{6}}{3} \), find \( AB \);  
(2) Find the maximum value of the area of \( \triangle ABC \).

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