
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
For positive integers  $m, n$  ( $m>n$ ),  $a_{n+1}, a_{n+2}, ..., a_m$   are non-negative integers that satisfy the following inequality.  $$  2> \frac{a_{n+1}}{n+1} \ge \frac{a_{n+2}}{n+2} \ge \cdots \ge \frac{a_m}{m} $$  Find the number of pair  $(a_{n+1}, a_{n+2}, \cdots, a_m)$ .

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