
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 the function $f(x) = e^{-x} - 2x - a$. If there exists a point $(x_0, y_0)$ on the curve $y = x^3 + x$ (where $x \in [-1, 1]$) such that $f(y_0) = y_0$, calculate the range of values for $a$.

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