
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 solution process and answer the questions:<br/>$\sqrt{1-\frac{3}{4}}=\sqrt{\frac{1}{4}}=\sqrt{(\frac{1}{2})^{2}}=\frac{1}{2}$; $\sqrt{1-\frac{5}{9}}=\sqrt{\frac{4}{9}}=\sqrt{(\frac{2}{3})^{2}}=\frac{2}{3}$; $\sqrt{1-\frac{7}{16}}=\sqrt{\frac{9}{16}}=\sqrt{(\frac{3}{4})^{2}}=\frac{3}{4}\ldots \ldots $<br/>$(1)$ Fill in the blanks: $\sqrt{1-\frac{9}{25}}=$______, $\sqrt{1-\frac{13}{49}}=$______.<br/>$(2)$ Calculate using the implied pattern above: $\sqrt{1-\frac{3}{4}}\cdot \sqrt{1-\frac{5}{9}}\cdot \sqrt{1-\frac{7}{16}}\ldots \ldots \sqrt{1-\frac{159}{6400}}$.

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