
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 $\overrightarrow {a} = (1, \sin\theta)$ and $\overrightarrow {b} = (3, 1)$.  
(1) When $\theta= \frac {\pi}{6}$, find the coordinates of the vector $2\overrightarrow {a} + \overrightarrow {b}$.  
(2) If $\overrightarrow {a} \parallel \overrightarrow {b}$ and $\theta \in (0, \frac {\pi}{2})$, find the value of $\sin(2\theta + \frac {\pi}{4})$.

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