
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 $P = 2^m$ and $Q = 5^n$. Determine which of the following expressions equals $20^{mn}$ for every pair of integers $(m, n)$:
A) $P^2Q$
B) $P^nQ^m$
C) $P^{n}Q^{2m}$
D) $P^{2m}Q^n$
E) $P^{2n}Q^m$
A) $P^2Q$
B) $P^nQ^m$
C) $P^nQ^{2m}$
D) $P^{2m}Q^n$
E) $P^{2n}Q^m$

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