
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
The function $f(x)$ is defined as follows:

$$
f(x) =
\begin{cases}
x^2 - 2x, & \text{if } x \geq 0 \\
\frac{1}{x}, & \text{if } x < 0
\end{cases}
$$

Given that $f(1) + f(a) = -2$, find the set of possible values for $a$.

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