
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:
(1) $0.027^{-\frac{1}{3}} - \left(-\frac{1}{7}\right)^{-2} + 256^{\frac{3}{4}} -3^{-1} + \left(\sqrt{2} - 1\right)^0$
(2) $\log_{2.5}6.25 + \lg 0.01 + \ln \sqrt{e} - 2^{1+\log_2 3}$
(3) $\lg 5^2 + \frac{2}{3}\lg 8 + \lg 5 \cdot \lg 20 + (\lg 2)^2$.

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