
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
How many positive integers  $n$  satisfy the inequality
\[
  \left\lceil \frac{n}{101} \right\rceil + 1 > \frac{n}{100} \, ?
\]
Recall that  $\lceil a \rceil$  is the least integer that is greater than or equal to  $a$ .

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