
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
Consider the function $y = f(x)$ defined as follows:
\[ f(x) = \begin{cases} 
x + 3 & \text{if } x \leq 0 \\
-x + 3 & \text{if } 0 < x \leq 3 \\
0 & \text{if } x > 3 
\end{cases} \]

For certain constants $a$, $b$, and $d$,
\[ h(x) = af(bx) + d. \]
The graph of $y = h(x)$ results from stretching $f(x)$ vertically by a factor of 2, horizontally by a factor of 3, and shifting it up by 5 units. Find the ordered triple $(a, b, d)$.

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