
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 replaced with the numbers $a-1, b+1,$ and $c^2$. After this, it turned out that the same numbers were on the board as initially (possibly in a different order). What values can the number $a$ take, given that the sum of the numbers $a, b,$ and $c$ is 2008? If necessary, round your answer to the nearest hundredth.

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