
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
Let \[g(x) = \left\{
\begin{array}{cl}
2ax+4, & \text{if } x > 3, \\
2x-6, & \text{if } 0 \le x \le 3, \\
3x - c, & \text{if } x < 0.
\end{array}
\right.\]
Find $a+c$ if the piecewise function $g(x)$ is continuous.

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