
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 $$( \sqrt {3}x-1)^{3}=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}$$, express $(a_{0}+a_{2})^{2}-(a_{1}+a_{3})^{2}$ in terms of $a_{0}$, $a_{1}$, $a_{2}$, and $a_{3}$.

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