
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 following:  
(1) $4(\sqrt{5}-4)^4 + 3(\sqrt{5}-4)^3 + 2^{-2}\times\left(2\frac{1}{4}\right)^{-\frac{1}{2}} - (0.01)^{0.5}$  
(2) $\frac{3a^{\frac{9}{2}}\sqrt{a^{-3}}}{\sqrt{\sqrt[3]{a^{-7}} \cdot \sqrt[3]{a^{13}}}}$．

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