
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 the complex numbers \( z_{1}, z_{2}, z_{3} \) satisfying:
\[
\begin{array}{l}
\left|z_{1}\right| \leq 1, \left|z_{2}\right| \leq 2, \\
\left|2z_{3} - z_{1} - z_{2}\right| \leq \left|z_{1} - z_{2}\right|.
\end{array}
\]
What is the maximum value of \( \left|z_{3}\right| \)?

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