
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 binomial expansion of (x^2 - $\frac {3}{x}$)^n, the binomial coefficient of the fifth term is the maximum and unique. Find the value of $C_{ n }^{ 0 }$ - $\frac {1}{2}$ $C_{ n }^{ 1 }$ + $\frac {1}{4}$ $C_{ n }^{ 2 }$ - ... + (-1)^n $\frac {1}{2}$ $C_{ n }^{ n }$.

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