
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 a pair of non-collinear vectors, if $\overrightarrow {a} = \overrightarrow {e}_{1} + \lambda \overrightarrow {e}_{2}$ and $\overrightarrow {b} = -2\lambda \overrightarrow {e}_{1} - \overrightarrow {e}_{2}$, and vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ are collinear, determine the value of $\lambda$.

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