
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 three vectors \\( \overrightarrow{a} \\), \\( \overrightarrow{b} \\), and \\( \overrightarrow{c} \\) in the same plane, where \\( \overrightarrow{a}=(1, 2) \\), \\( \overrightarrow{b}=(-2, 3) \\), and \\( \overrightarrow{c}=(-2, m) \\):  
(1) If \\( \overrightarrow{a} \perp ( \overrightarrow{b} + \overrightarrow{c}) \\), find the value of \\( m \\);  
(2) If \\( k \overrightarrow{a} + \overrightarrow{b} \\) is collinear with \\( 2 \overrightarrow{a} - \overrightarrow{b} \\), find the value of \\( k \\).

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