
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 $$f(x)=\sin(\frac{\pi}{4}+x)\sin(\frac{\pi}{4}-x)+\sqrt{3}\sin x\cos x\ (x\in\mathbb{R})$$.
(1) Find the value of $f(\frac{\pi}{6})$;
(2) Let A, B, C be the three internal angles of △ABC. If $f(\frac{A}{2})=1$, find the maximum value of $\sin B + \sin C$.

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