
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 $f(x)=A\sin (\omega x+\varphi)$ ($A > 0$, $\omega > 0$, $|\varphi| < \frac {\pi}{2}$) satisfies the following conditions:  
1. The period $T=\pi$;  
2. The graph, after being shifted to the left by $\frac {\pi}{6}$ units, is symmetric about the $y$-axis;  
3. $f(0)=1$.  
(I) Find the expression of the function $f(x)$;  
(II) Let $\alpha, \beta \in (0, \frac {\pi}{4})$, $f(\alpha- \frac {\pi}{3})= -\frac {10}{13}$, $f(\beta+ \frac {\pi}{6})= \frac {6}{5}$, find the value of $\cos (2\alpha-2\beta)$.

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