
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
Determine the value of \( \sqrt{a} \div \sqrt{b} \) using the following information:
$$
\frac{\left(\frac{3}{5}\right)^2 + \left(\frac{2}{7}\right)^2}{\left(\frac{2}{9}\right)^2 + \left( \frac{1}{6} \right)^2} = \frac{28a}{45b}
$$

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