
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. Evaluate \( 1.40 \frac{(x+1)^{-\frac{1}{2}}}{(x-1)^{-\frac{1}{2}}-(x+1)^{-\frac{1}{2}}} \) given \( x=\frac{a^{2}+1}{2a} \).

2. Simplify \( 1.41 \left( \frac{\left(x+\sqrt[3]{2ax^{2}}\right)\left(2a+\sqrt[3]{4a^{2}x}\right)^{-1} - 1}{\sqrt[3]{x} - \sqrt[3]{2a}} - (2a)^{-\frac{1}{3}} \right)^{-6} \).

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