
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 $z= \frac {1}{2}+ \frac { \sqrt {3}}{2}i$, find the value of $a_2$ in the expression $(x-z)^4=a_0x^4+a_1x^3+a_2x^2+a_3x+a_4$.

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