
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
Let \( A = \frac{\sqrt{a+2 \sqrt{b}+\frac{b}{a}} \cdot \sqrt{2 a-10 \sqrt[6]{8 a^{3} b^{2}}+25 \sqrt[3]{b^{2}}}}{a \sqrt{2 a}+\sqrt{2 a b}-5 a \sqrt[3]{b}-5 \sqrt[6]{b^{5}}} \).

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