
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 were numbers \( a, b, \) and \( c \) written on the board. They were erased and replaced with the numbers \( a-1, b+1, c^2 \). After this, it turned out that the same numbers (possibly in a different order) were written on the board again. What values can the number \( a \) take if it is known that the sum of the numbers \( a, b, \) and \( c \) is 2005? If necessary, round the answer to two decimal places.

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