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

(2) $\lg 5 \cdot \lg 20 - \lg 2 \cdot \lg 50 - \lg 25$

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