
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 the positive integers \( a_1, a_2, \ldots, a_{2005} \) form a strictly increasing sequence. For all distinct \( i, j, k \) less than 2005, \( a_i a_j \neq a_k \). Find the minimum possible value of \( a_{2005} \).

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