
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 complex numbers \( z_{1}, z_{2}, z_{3} \) such that \( \left|z_{1}\right| \leq 1 \), \( \left|z_{2}\right| \leq 1 \), and \( \left|2 z_{3}-\left(z_{1}+z_{2}\right)\right| \leq \left|z_{1}-z_{2}\right| \). What is the maximum value of \( \left|z_{3}\right| \)?

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