
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
1. Calculate: $(1)0.027\;^{- \frac {1}{3}}+ (\sqrt {8})\;^{\frac {4}{3}}-3^{-1}+ (\sqrt {2}-1)^{0}$
2. Calculate: $(2)\lg 25+ \lg 4+ 7\;^{\log _{7}2}+ \log _{2}3 \cdot \log _{3}4.$

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