
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
101. Write the number 100 using six non-zero identical digits in such a way that the method of writing does not depend on the digits used.

102. Calculate:

\(\lg \operatorname{tg} 37^{\circ} \cdot \lg \operatorname{tg} 38^{\circ} \cdot \lg \operatorname{tg} 39^{\circ} \ldots \lg \operatorname{tg} 47^{\circ}\)

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