
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

You are asked to think of any integer between 1 and 100 and then successively divide it by 3, 5, and 7, reporting each time the remainder. Given this information, the one who asked the question will immediately tell you the number you thought of.

Can the reader devise a simple method to perform this feat mentally? If not, they may be interested to learn how the ancient mathematician did it.

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