
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
Expand $(2- \sqrt{3}x)^{50}$ as $a_0 + a_1x + a_2x^2 + \ldots + a_{50}x^{50}$, where $a_0, a_1, a_2, \ldots, a_{50}$ are constants. Calculate $(a_0 + a_2 + \ldots + a_{50}) - (a_1 + a_3 + a_5 + \ldots + a_{49}) = \_\_\_\_\_\_$.

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