
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
Read the following material and answer the questions:<br/>【Scenario】During a math activity class, the teacher led the students in a practical activity of "finding the arithmetic square root of a positive number using a rule."<br/>【Practical Exploration】The students used a calculator to calculate the arithmetic square roots in the table below and organized the data as follows:<br/><table class="edittable"><tbody><tr><td width="40">$\ldots $</td><td width="238">$\sqrt{0.0625}$</td><td width="221">$\sqrt{0.625}$</td><td width="204">$\sqrt{6.25}$</td><td width="204">$\sqrt{62.5}$</td><td width="196">$\sqrt{625}$</td><td width="213">$\sqrt{6250}$</td><td width="230">$\sqrt{62500}$</td><td width="40">$\ldots $</td></tr><tr><td>$\ldots $</td><td>$0.25$</td><td>$0.791$</td><td>$2.5$</td><td>$7.91$</td><td>$25$</td><td>$79.1$</td><td>$250$</td><td>$\ldots $</td></tr></tbody></table>$(1)$Based on the above exploration, the rule for the change in the decimal point between the number being square rooted and its arithmetic square root is: if the decimal point of the number being square rooted moves ______ places to the right or left, then the decimal point of its arithmetic square root moves ______ places to the right or left accordingly:<br/>$(2)$Given $\sqrt{3}≈1.732$, please directly write the values of the following expressions using the above rule: $\sqrt{0.03}\approx $______,$\sqrt{300}≈$______.<br/>$(3)$Can you determine the value of $\sqrt{30}$ based on the value of $\sqrt{3}$? Please explain your reasoning.

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