
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
For constants $a$ and $b,$ consider the function $f(x)$ given by
\[
f(x) = \left\{
\begin{array}{cl}
2ax + b & \text{if } x \leq 0, \\
7 - 2x & \text{if } x > 0.
\end{array}
\right.
\]
The function $f$ has the property that $f(f(x)) = x$ for all $x$ in its domain. Determine $a + b.$

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