
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 sum of several not necessarily distinct positive numbers did not exceed 100. Each of these numbers was replaced by a new number in the following way: first, they were logarithmed to base 10, then rounded to the nearest integer, and finally, 10 was raised to the power of the resulting integer. Could it happen that the sum of the new numbers exceeds 300?

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