
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 respectively a, b, c, and $\cos C= \frac {3}{5}$.
(1) Find the value of $\sin(C+ \frac {\pi}{3})$;
(2) If $\overrightarrow {CA} \cdot \overrightarrow {CB} = 9$, $a+b=8$, find the value of side c and the area of $\triangle ABC$.

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