
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
If the vector $λ \vec{e_1} - \vec{e_2}$ is collinear with $\vec{e_1} - λ \vec{e_2}$, where $\vec{e_1}$ and $\vec{e_2}$ are non-collinear unit vectors, then the value of the real number $λ$ is ______.

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