
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
Three numbers $a$, $b$, and $c$ were written on a board. They were erased, and instead, the numbers $a-2$, $b+2$, and $c^{2}$ were written. After this, it turned out that the same numbers were written on the board as at the beginning (possibly in a different order). 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 the nearest hundredth.

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