
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
The graph of \(y = f(x)\) as previously defined passes through specific transformations to create a new graph \(y = g(x)\). The new graph is obtained by compressing \(f(x)\) vertically by a factor of \(\frac{1}{2}\), stretching it horizontally by a factor of \(3\), and shifting it downward by 3 units. Determine the new formula for \(g(x)\) and identify the ordered triple \((a, b, c)\).

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