
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
Let \( a \) be a real number and \( b \) be a real number with \( b \neq -1 \) and \( b \neq 0 \). Determine all pairs \((a, b)\) for which 

\[ 
\frac{(1+a)^{2}}{1+b} \leq 1+\frac{a^{2}}{b}
\]

is satisfied. For which pairs \( (a, b) \) does equality hold?

(Walther Janous)

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