
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 a positive integer  $n$ , there are positive integers  $a_1, a_2, ... a_n$  that satisfy these two.
(1)  $a_1=1, a_n=2020$ (2) for all integer  $i$ ,  $i$ satisfies  $2\leq i\leq n, a_i-a_{i-1}=-2$  or  $3$ .
find the greatest  $n$ 

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