
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 $$f(x)=\sin(2x- \frac {\pi}{6})-\cos(2x+ \frac {\pi}{3})+a$$  
(1) Stretch the x-coordinates of all points on the graph of $y=f(x)$ to twice their original length (keeping the y-coordinates unchanged), and then shift all points on the resulting graph to the left by $$\frac {\pi}{3}$$ units to get the graph of $y=g(x)$. Find the expression for the function $y=g(x)$.  
(2) The sum of the maximum and minimum values of $y=g(x)$ on $$[0, \frac {\pi}{2}]$$ is 5. Find the value of $a$.

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