
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 $\overrightarrow{a}=(\sin \theta, 2)$ and $\overrightarrow{b}=(\cos \theta, 1)$, which are collinear, where $\theta \in (0, \frac{\pi}{2})$.
1. Find the value of $\tan (\theta + \frac{\pi}{4})$.
2. If $5\cos (\theta - \phi)=3 \sqrt{5}\cos \phi, 0 < \phi < \frac{\pi}{2}$, find the value of $\phi$.

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