
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
In the complex plane, the complex numbers \( z_1, z_2, z_3 \) satisfy:
\[ 
z_{1}=\lambda z_{2}(\lambda<0),\left|z_{1}-z_{2}\right|=13, 
\]
\[
\left|z_{1}\right|^{2}+\left|z_{3}\right|^{2}+\left|z_{1} z_{3}\right|=144, 
\]
\[
\left|z_{2}\right|^{2}+\left|z_{3}\right|^{2}-\left|z_{2} z_{3}\right|=25 .
\]

Then \( \left|z_{3}\right| = \)

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