
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
Let the function be $$f(x)=\cos(2x+ \frac {\pi}{3})+\sin^{2}x$$.
(1) Find the maximum value of the function $y=f(x)$ and its smallest positive period;
(2) Let $A$, $B$, and $C$ be the three interior angles of $\triangle ABC$. If $$\cos B= \frac {1}{3}$$ and $$f\left( \frac {C}{3}\right)=- \frac {1}{4}$$, find $\sin A$.

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