
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
$(1)$ Fill in the blanks: $\sqrt{9} \times \sqrt{16}=$______, $\sqrt{9 \times 16}=$______; $\sqrt{25} \times \sqrt{36}=$______, $\sqrt{25 \times 36}=$______.<br/>$(2)$ Calculate according to the above rules:<br/>① $\sqrt{6} \times \sqrt{24}$;<br/>② $\sqrt{1\frac{2}{3}} \times \sqrt{9\frac{3}{5}}$.<br/>$(3)$ Given $a=\sqrt{2}$, $b=\sqrt{10}$, express $\sqrt{40}$ in terms of $a$ and $b$.

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