
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
Given the equation $A \log_{100} 5 + B \log_{100} 2 = C$, find the values of positive integers $A$, $B$, and $C$ which have no common factor greater than 1, and calculate $A + B + C$.

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