
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
Simplify and find the value of the following expressions:<br/>$(1)$ Simplify $\sqrt{{(\pi-5)}^{2}}-\sqrt[3]{{(2-\pi)}^{3}}$ and find its value;<br/>$(2)$ Calculate: $0.06{4}^{-\frac{1}{3}}+{(-\frac{5}{2})}^{0}-{(2\frac{1}{4})}^{\frac{1}{2}}+0．{1}^{-2}$.

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