
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
For various nonzero real numbers \(a, b, c\), the following equalities hold:

\[ a + \frac{2}{b} = b + \frac{2}{c} = c + \frac{2}{a} = d \]

Find all possible values of the number \(d\).

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