
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 $y = f(x)$ is the same described in the original problem. Now, consider the new function defined by 
\[ h(x) = a f(bx) + c \]
The graph of $y = h(x)$ is created by shrinking the graph of $y = f(x)$ horizontally by a factor of 4 and vertically by a factor of 1/3, and then shifted up by 1 unit.

Determine the values of the constants \(a\), \(b\), and \(c\) in the function \(h(x)\).

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