
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 in the plane: \\( \overrightarrow{a}=(3\,,\,2) \\) , \\( \overrightarrow{b}=(-1\,,\,2) \\) , \\( \overrightarrow{c}=(4\,,\,1) \\)
(1) If \\( (\overrightarrow{a}+λ\overrightarrow{c}) \parallel (2 \overrightarrow{b}- \overrightarrow{a}) \\) , find the real number \\( λ \\) ;
(2) If \\( (\overrightarrow{a}+λ\overrightarrow{c}) \perp (2 \overrightarrow{b}- \overrightarrow{a}) \\) , find the real number \\( λ \\) .

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