
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 the function $f(x) = e^x + 2x - a$, where $a \in \mathbb{R}$, if there exists a point $(x_0, y_0)$ on the curve $y = \sin x$ such that $f(f(y_0)) = y_0$, then the range of values for the real number $a$ is ______.

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