
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
Let $\heartsuit(x)$ denote the product of the digits of the positive integer $x$. For instance, $\heartsuit(42) = 4 \cdot 2 = 8$. Determine the number of two-digit values of $x$ that satisfy $\heartsuit(\heartsuit(x)) = 6$.

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