
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
Modify the initial terms of the sequence to start with $500$ instead of $1000, x,$ and continuing with the difference between the two latest terms, as in $500, x, 500 - x, \ldots$ until a negative term. Determine the value of $x$ such that the length of the sequence of positive numbers is maximized.

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