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

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