
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 $$\overrightarrow {OM}=(\cos\alpha，\sin\alpha)， \overrightarrow {ON}=(\cos x，\sin x)， \overrightarrow {PQ}=(\cos x，-\sin x+ \frac {4}{5\cos\alpha})$$  
(1) When $$\cos\alpha= \frac {4}{5\sin x}$$, find the smallest positive period of the function $$y= \overrightarrow {ON}\cdot \overrightarrow {PQ}$$;  
(2) When $$\overrightarrow {OM}\cdot \overrightarrow {ON}= \frac {12}{13}$$ and $$\overrightarrow {OM}$$ is parallel to $$\overrightarrow {PQ}$$, and both $\alpha-x$ and $\alpha+x$ are acute angles, find the value of $\cos 2\alpha$.

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