
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) Compute the expression $\frac{1}{ \sqrt{2}-1}-\left(\frac{3}{5} \right)^{0}+\left(\frac{9}{4} \right)^{-0.5}+ \sqrt[4]{( \sqrt{2}-e)^{4}}$;

(2) Compute the expression $\lg 500+\lg \frac{8}{5}- \frac{1}{2}\lg 64+50×(\lg 2+\lg 5)^{2}$.

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