
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 expressions:

$(1) 5^{2\log_5{3}} + \log_4{32} - \log_3(\log_2{8})$

$(2) {0.027}^{-\frac{1}{3}} - {(-\frac{1}{6})}^{-2} + {256}^{0.75} + {(\frac{1}{\sqrt{3}-1})}^{0}$

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