
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 certain constants $a,$ $b,$ and $c,$
\[ g(x) = af(bx) + c. \]
Given the graph of $y = f(x)$ described by segments and transformations, determine the values of $a,$ $b,$ and $c,$ if the graph of $y = g(x)$ is obtained by compressing the graph of $y = f(x)$ horizontally by a factor of 3 and shifting it downward by 2 units.

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