
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 $\overrightarrow{a}=(2\sin \alpha,1)$, $\overrightarrow{b}=(\cos \alpha,1)$, $\alpha \in (0, \frac{\pi}{4})$.
(1) If $\overrightarrow{a} \parallel \overrightarrow{b}$, find the value of $\tan \alpha$;
(2) If $\overrightarrow{a} \cdot \overrightarrow{b} = \frac{9}{5}$, find the value of $\sin(2\alpha + \frac{\pi}{4})$.

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