
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
A sequence of positive integers \( a_{1}, a_{2}, \ldots, a_{2017} \) has the property that for all integers \( m \) where \( 1 \leq m \leq 2017 \), \( 3\left(\sum_{i=1}^{m} a_{i}\right)^{2} = \sum_{i=1}^{m} a_{i}^{3} \). Compute \( a_{1337} \).

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