
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 the following expressions:

$(1)\left( \left( 2 \frac{3}{5} \right)^{0} +2^{-2}\cdot\left( 2 \frac{1}{4} \right)^{-\frac{1}{2}} -(0.01)^{0.5}\right)$;

$(2) \frac{5}{6}a^{\,\frac{1}{3}} \cdot b^{-2}\cdot\left(\begin{matrix}-3a\\begin{matrix}^{-\frac{1}{2}} \\\\ \; \\; \\; \\; \\; \\; \\; \\; \\; \\\end{matrix}b^{-1}\end{matrix}\right) \div\left(\begin{matrix}4a\\begin{matrix}^{\frac{2}{3}} \\\\ \; \\; \\; \\\end{matrix}\cdot b^{-3}\end{matrix}\right)^{\frac{1}{2}} (a,b > 0)$.

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