
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 the first term is $2500$, the second term is $y$, and subsequent terms follow the rule that each term is the subtraction of the previous two terms: $a_{n} = a_{n-2} - a_{n-1}$. The sequence stops once a negative term appears. Find the positive integer $y$ that maximizes the number of terms in the sequence before a negative term is encountered.

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