
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 $P(m)$ denote the number of ways to express the positive integer $m$ as a product\[m = g_1 \times g_2 \times \ldots \times g_j\], where $j \geq 1$, each $g_i$ are integers strictly greater than 1, and the sequence order matters. Calculate $P(144)$, which has multiple factorings in combinations considering factor counts and their arrangements.
A) 104
B) 113
C) 122
D) 131

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