
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 $\triangle ABC$, it is known that $\cos A= \frac {5}{13}$, $\tan \frac {B}{2} + \cot \frac {B}{2} = \frac {10}{3}$, and $c=21$.  
(1) Find the value of $\cos(A-B)$.  
(2) Find the area of $\triangle ABC$.

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