
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
There are 5555 children, numbered 1 to 5555, sitting around a circle in order. Each child has an integer in hand: the child numbered 1 has the integer 1, the child numbered 12 has the integer 21, the child numbered 123 has the integer 321, and the child numbered 1234 has the integer 4321. It is known that the sum of the integers held by any 2005 consecutive children is equal to 2005. What is the integer held by the child numbered 5555?

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