
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
What is the value of \[\left(\sum_{k=1}^{50} \log_{10^k} 2^{k^2}\right)\cdot\left(\sum_{k=1}^{10} 3^k \log_{27^k} 125^k\right)?\]
A) $752986 \qquad$
B) $75298600 \qquad$
C) $752986000 \qquad$
D) $7529860 \qquad$
E) $59048$

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