
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
There are 100 coins, out of which 99 are real and identical in weight, and 1 is a counterfeit that is lighter than the others. Dmitry has a balance scale that always shows an incorrect result (for example, if the left pan is heavier, it will show either equality or that the right pan is heavier, but it is unknown which one). Help Dmitry find 98 real coins.

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