
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
Initially, the numbers \(a\), \(b\), and \(c\) were written on the board. They were erased and replaced with the numbers \(a-2\), \(b+2\), and \(c^2\). After this, it turned out that the same three numbers were on the board again (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 2006? If necessary, round the answer to two decimal places.

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