
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
Simplify the following expressions:

$(1)$ $(0.027)^{-\frac{1}{3}} - \left(\frac{1}{7}\right)^{-2} + \left(2\frac{7}{9}\right)^{\frac{1}{2}} - \left(\sqrt{2} - 1\right)^{0}$

$(2)$ $\log_{3}\frac{\sqrt[4]{27}}{3} + \lg 25 + \lg 4 + 7^{\log_{7}2}$

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