
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 \( \alpha \) and \( \beta \) be complex numbers such that \( |\beta| = 1 \) and \( \overline{\alpha} \beta \neq 1 \). Additionally, let \( c \) be a real number such that \( \overline{\alpha}\beta + c \neq 1 \) and \( |c| < 1 \). Find the maximum possible value of
\[
\left| \frac{\beta - \alpha}{1 - \overline{\alpha} \beta + c} \right|.
\]

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