
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 $\overrightarrow{b}=(1,2)$.

$(1)$ If $\overrightarrow{a} \parallel \overrightarrow{b}$, find the value of $\tan \theta$;  
$(2)$ If $|\overrightarrow{a}|=|\overrightarrow{b}|, 0 < \theta < \pi$, find the value of $\theta$.

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