
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
Consider a sequence where each term after the first two is obtained by subtracting the preceding term from the one before that. The sequence's first two terms are $5000, x, 5000 - x, \ldots$ and the last term of the sequence is the first negative term. Determine the positive integer $x$ that produces a sequence of maximum length.

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