
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 two distinct 2-digit numbers is equal to 120, and the decimal number obtained by placing one of the two integers before the decimal point and the other after the decimal point exactly divides the sum of these two integers. Find the greater of the two integers.

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