
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
Given the function $$f(x)=\sin(x+ \frac {\pi}{2})\cos(x- \frac {\pi}{3})$$.
(1) Find the smallest positive period of the function $f(x)$.
(2) The graph of the function $y=f(x)$ is translated downwards by $$\frac {1}{4}$$ units, and then the vertical coordinates of each point on the graph are stretched to 4 times their original value (the horizontal coordinates remain unchanged), resulting in the graph of the function $y=g(x)$. Find the maximum value of the function $y=g(x)$ on the interval $$[0, \frac {\pi}{3}]$$.

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