
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 \(\overrightarrow{a}=(1, \sqrt{3})\) and \(\overrightarrow{b}=(2,m)\),
(1) when \(3\overrightarrow{a}-2\overrightarrow{b}\) is perpendicular to \(\overrightarrow{a}\), find the value of \(m\);
(2) when the angle between \(\overrightarrow{a}\) and \(\overrightarrow{b}\) is \(120^{\circ}\), find the value of \(m\).

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