
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 \( c \) and \( d \), let \[ g(x) = \left\{
\begin{array}{cl}
cx + d & \text{if } x < 3, \\
10 - 2x & \text{if } x \ge 3.
\end{array}
\right.\] The function \( g \) has the property that \( g(g(x)) = x \) for all \( x \). What is \( c + d \)?

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