
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
$P = a_{1} a_{2} \cdots a_{n}$ is the product of $n$ numbers. Based on the associative property of multiplication, without altering its order, using only parentheses to indicate the order of multiplication, how many distinct multiplication schemes are there?

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