
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 \( \gamma \) and \( \delta \) be complex numbers such that \( |\delta| = 1 \) and \( \overline{\gamma} \delta \neq -1. \) Find the maximum value of
\[
\left| \frac{\delta + \gamma}{1 + \overline{\gamma} \delta} \right|.
\]

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