
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 $A$, $B$, and $C$ are denoted as $a$, $b$, and $c$ respectively.  
(1) If $a$, $b$, $c$ form a geometric sequence, and $\cos B= \frac {12}{13}$, find the value of $\frac {\cos A}{\sin A}+ \frac {\cos C}{\sin C}$.  
(2) If $A$, $B$, $C$ form an arithmetic sequence, and $b=2$, let $A=\alpha$, and the perimeter of $\triangle ABC$ be $l$, find the maximum value of $l=f(\alpha)$.

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