
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
Determine the value of \[\left(\sum_{k=1}^{10} \log_{7^k} 2^{2k}\right) \cdot \left(\sum_{k=1}^{50} \log_{4^k} 16^k\right).\]
A) $200 \log_2 7$
B) $4000 \log_7 2$
C) $200 \log_7 2$
D) $10000 \log_7 2$
E) $8000 \log_2 7$

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