
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 $f(x)=\sin (\omega x+\varphi)$ ($\omega > 0$, $|\varphi| < \frac{\pi}{2}$) satisfies $f(x+ \frac{\pi}{2})=-f(x)$, if its graph is shifted to the left by $\frac{\pi}{6}$ units, the resulting function is an odd function.  
(1) Find the analytical expression of $f(x)$.  
(2) In an acute triangle $ABC$, where the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and it satisfies $(2c-a)\cos B=b\cos A$, find the range of values for $f(A)$.

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