
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
Let $\overrightarrow{e_1}$ and $\overrightarrow{e_2}$ be two mutually perpendicular unit vectors, and $\overrightarrow{a} = -(2\overrightarrow{e_1} + \overrightarrow{e_2})$, $\overrightarrow{b} = \overrightarrow{e_1} - \lambda\overrightarrow{e_2}$.
(1) If $\overrightarrow{a} \parallel \overrightarrow{b}$, find the value of $\lambda$;
(2) If $\overrightarrow{a} \perp \overrightarrow{b}$, find the value of $\lambda$.

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