
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
Suppose \( P = 2^m \) and \( Q = 5^n \). Which of the following is equal to \( 10^{m+n} \) for every pair of integers \((m, n)\)?
- without choices -
A) \( P^n \cdot Q^m \)
B) \( P^{n+1} \cdot Q^{m+1} \)
C) \( P \cdot Q \cdot 2^n \cdot 5^m \)
D) \( P^m \cdot Q^n \)
E) \( P^{n+1} \cdot Q \cdot 2^m \)

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