
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 \( a, b \), and \( c \) be complex numbers such that \( |a| = |b| = |c| = |a + b + c| = 1 \). If \( |a - b| = |a - c| \) and \( b \neq c \), evaluate \( |a + b| |a + c| \).

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