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

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