
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 some positive integer  $n$ , there exists  $n$  different positive integers  $a_1, a_2, ..., a_n$  such that $(1)$   $a_1=1, a_n=2000$  $(2)$   $\forall i\in \mathbb{Z}$    $s.t.$    $2\le i\le n, a_i -a_{i-1}\in \{-3,5\}$ Determine the maximum value of n.

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