
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and they satisfy $(3b-c)\cos A - a\cos C = 0$.
(1) Find $\cos A$;
(2) If $a = 2\sqrt{3}$ and the area of $\triangle ABC$ is $S_{\triangle ABC} = 3\sqrt{2}$, determine the shape of $\triangle ABC$ and explain the reason;
(3) If $\sin B \sin C = \frac{2}{3}$, find the value of $\tan A + \tan B + \tan C$.

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