
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 that $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ are two non-collinear vectors on a plane, and $\overrightarrow{MN} = 2\overrightarrow{e_{1}} - 3\overrightarrow{e_{2}}$, $\overrightarrow{NP} = \lambda \overrightarrow{e_{1}} + 6\overrightarrow{e_{2}}$, and points $M$, $N$, and $P$ are collinear, determine the value of $\lambda$.

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