
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 $|\overrightarrow{a}|=2, |\overrightarrow{b}|=2$,<br/>(1) If $\overrightarrow{a} \parallel \overrightarrow{b}$, find $\overrightarrow{a} \cdot \overrightarrow{b}$;<br/>(2) If the projection vector of vector $\overrightarrow{a}$ onto vector $\overrightarrow{b}$ is $-\frac{\overrightarrow{b}}{|\overrightarrow{b}|}$, find the angle $\theta$ between $\overrightarrow{a}$ and $\overrightarrow{b}$;<br/>(3) Under the condition in (2), if $(\overrightarrow{a}-m\overrightarrow{b}) \perp \overrightarrow{a}$, find the value of $m$.

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