
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 some constants $a$ and $b,$ let \[g(x) = \left\{
\begin{array}{cl}
ax + b & \text{if } x < 3, \\
9 - 2x & \text{if } x \ge 3.
\end{array}
\right.\]
The function $g$ has the property that $g(g(x)) = x$ for all $x.$ Additionally, $g(x)$ is continuous at $x = 3$. What is $a + b?$

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