
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
For any complex numbers $w_{1}$, $w_{2}$, define ${{w}_{1}}*{{w}_{2}}={{w}_{1}}\overline{{{w}_{2}}}$, where $\overline{{{w}_{2}}}$ is the conjugate of $w_{2}$. For any complex numbers $z_{1}$, $z_{2}$, $z_{3}$, the following four propositions are given:

1. $(z_{1}+z_{2})*z_{3}=(z_{1}*z_{3})+(z_{2}*z_{3})$;
2. $z_{1}*(z_{2}+z_{3})=(z_{1}*z_{2})+(z_{1}*z_{3})$;
3. $(z_{1}*z_{2})*z_{3}=z_{1}*(z_{2}*z_{3})$;
4. $z_{1}*z_{2}=z_{2}*z_{1}$.

Then, the true propositions are __________. (Fill in the numbers of all true propositions)

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