
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
Calculate the value of the expression in part a) and simplify the expressions in parts b) and c):

a) \(0.027^{-\frac{1}{3}}-\left(-\frac{1}{6}\right)^{-2}+256^{0.75}+0.25^{0}+(-0.5)^{-5}-3^{-1}\).

b) \(\left[\frac{\left(a^{\frac{3}{4}}-b^{\frac{3}{4}}\right)\left(a^{\frac{3}{4}}+b^{\frac{3}{4}}\right)}{a^{\frac{1}{2}}-b^{\frac{1}{2}}}-\sqrt{a b}\right] \cdot \frac{2 \cdot \sqrt{2.5}(a+b)^{-1}}{(\sqrt{1000})^{\frac{1}{3}}}\).

c) \(\left\{1-\left[x\left(1+x^{2}\right)^{-\frac{1}{2}}\right]^{2}\right\}^{-1} \cdot\left(1+x^{2}\right)^{-1} \cdot\left[x^{0}\left(1+x^{2}\right)^{-\frac{1}{2}}-x^{2}\left(1+x^{2}\right)^{-\frac{1}{2}}\right]\).

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