
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
Given the piecewise function:
\[ f(x) = 
  \begin{cases} 
   -x-3 & \text{if } -4 \leq x \leq -1 \\
   x^2 - 1 & \text{if } -1 < x < 2 \\
   3 - x & \text{if } 2 \leq x \leq 4 
  \end{cases} \]

Define a new function $g(x)$ by the equation:
\[ g(x) = 2f(3x) + 5 \]

Sketch the graph of $y = g(x)$ and determine the constants $a$, $b$, and $c$ such that $g(x) = af(bx) + c$.

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