
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 $$(2- \sqrt {3}x)^{50} = a_{0}+a_{1}x+a_{2}x^{2}+\ldots+a_{50}x^{50},$$ where $a_{0}, a_{1}, a_{2}, \ldots, a_{50}$ are constants, calculate $$(a_{0}+a_{2}+a_{4}+\ldots+a_{50})^{2}-(a_{1}+a_{3}+a_{5}+\ldots+a_{49})^{2} = \_\_\_\_\_\_.$$

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