
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
:
The logarithm of 55 with base 50 and the logarithm of 20 with base 55 are given. Calculate the logarithm of \(2662 \sqrt{10}\) with base 250 using these values.

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