
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
Let  $ 0 < a_1 < a_2 < a_3 < ... < a_{10000} < 20000$  be integers such that  $ gcd(a_i,a_j) < a_i, \forall i < j$  ; is  $ 500 < a_1$  *(always)* true ?

*(own)*  :lol:

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