
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 $\overrightarrow{a} = (\sin\theta, \cos\theta - 2\sin\theta)$ and $\overrightarrow{b} = (2, 1)$:
1. If $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$, find the value of $\tan\theta$.
2. If $\lvert \overrightarrow{a} \rvert = \lvert \overrightarrow{b} \rvert$ and $\frac{\pi}{4} < \theta < \pi$, find the value of $\theta$.

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