
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
In a counting game devised by Travis, Tadd, Todd, and Tucker are required to count numbers in turns, with each child increasing the count of numbers they say by two more than the last time they spoke, until the number 1000 is reached. Determine the 250th number said by Tadd.

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