
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 vectors $$\overrightarrow {a}=(2，\sin{\theta})， \overrightarrow {b}=(1，\cos{\theta})$$, where $\theta$ is an acute angle.
(1) If $$\overrightarrow {a}\cdot \overrightarrow {b}= \frac {13}{6}$$, find the value of $\sin{\theta}+\cos{\theta}$;
(2) If $$\overrightarrow {a}∥ \overrightarrow {b}$$, find the value of $\cos{2\theta}$.

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