
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
The function \( f \) is defined on integers and takes integer values, moreover \( f(x) \neq x \) for every integer \( x \). We call a number \( a \) curious if for any integer \( x \) the equality \( f(x) = f(a - x) \) holds. Can each of the numbers 60, 62, and 823 be curious?

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