
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
(I) Find the constant term in the expansion of ${({x}^{2}-\frac{1}{2\sqrt{x}})}^{10}$;

(II) Given that ${(2x-\sqrt{3})}^{10}={a}_{0}+{a}_{1}x+{a}_{2}{x}^{2}+\cdots +{a}_{10}{x}^{10}$, find $({a}_{0}+{a}_{1}+{a}_{2}+{a}_{3}+\cdots +{a}_{10})({a}_{0}-{a}_{1}+{a}_{2}-{a}_{3}+\cdots +{a}_{10})$.

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