
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
\[ 1.22 \frac{(\sqrt{a}+\sqrt{b})^{2}-4 b}{(a-b):\left(\sqrt{\frac{1}{b}}+3 \sqrt{\frac{1}{a}}\right)}: \frac{a+9 b+6 \sqrt{a b}}{\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}}} \]

\[ 1.23\left(\frac{\left(z^{\frac{2}{p}}+z^{\frac{2}{q}}\right)^{2}-4 z^{\frac{2}{p}+\frac{2}{q}}}{\left(z^{\frac{1}{p}}-z^{\frac{1}{q}}\right)^{2}+4 z^{\frac{1}{p}+\frac{1}{q}}}\right)^{\frac{1}{2}} \]

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