
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 number $z= \frac{1+i}{1-i}$ (where $i$ is the imaginary unit), find the value of $C_{ 8 }^{ 1 }$+ $C_{ 8 }^{ 2 }$•z+ $C_{ 8 }^{ 3 }$•z<sup>2</sup>+ $C_{ 8 }^{ 4 }$•z<sup>3</sup>+ $C_{ 8 }^{ 5 }$•z<sup>4</sup>+ $C_{ 8 }^{ 6 }$•z<sup>5</sup>+ $C_{ 8 }^{ 7 }$•z<sup>6</sup>+ $C_{ 8 }^{ 8 }$•z<sup>7</sup>.

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