
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
1. Compute the integral: $\int\_{0}^{1} \sqrt{1-{x}^{2}}dx =$\_\_\_\_\_\_\_.
2. A particle moves along a straight line with velocity $v(t) = t^2 - 4t + 3(m/s)$ starting from time $t = 0(s)$. Find the distance traveled by the particle at time $t = 4$.
3. Let $f(x) = x^3 - \frac{1}{2}x^2 - 2x + 5$. If there exists a real number $x \in [-1, 2]$ such that $f(x) > m$ holds, find the range of values for the real number $m$.
4. Let $f(x)$ be an odd function defined on $\mathbb{R}$ such that $f(2) = 0$ and $xf'(x) - f(x) = 0$ when $x > 0$. Find the solution set for the inequality $x^{2} - f(x) > 0$.

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