
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 $$f(x)=2\sin^{2}\left( \frac {\pi}{4}+x\right)+ \sqrt {3}\cos2x-1$$, where $x\in\mathbb{R}$.  
(1) Find the smallest positive period of the function $f(x)$.  
(2) In $\triangle ABC$, if $f(C)= \sqrt {3}$ and $2\sin B=\cos(A-C)-\cos(A+C)$, find the value of $\tan A$.

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