
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 \[f(x) = \left\{
\begin{array}{cl} 
2ax+6, & \text{ if } x > 2, \\
3x-2 & \text{ if } -2 \leq x \leq 2, \\
4x+2c & \text{ if } x < -2.
\end{array} 
\right.\] Determine the value of $a+c$ if the piecewise function $f(x)$ is continuous.

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