
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
Given that \( a \) and \( b \) are real numbers with their product \( ab = 1 \), and:

$$
\frac{a+b+2}{4} = \frac{1}{a+1} + \frac{1}{b+1}
$$

Determine the values of \( a \) and \( b \).

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