
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 $e_{1}$ and $e_{2}$ be two non-collinear vectors, and $a=e_{1}+\lambda e_{2}$ is collinear with $b=- \frac{1}{3}e_{2}-e_{1}$, calculate the real number $\lambda$.

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