
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
Given the exponential growth equation $\lg X_{n}=n\lg \left(1+p\right)+\lg X_{0}$, where $X_{0}$ is the initial quantity of DNA, and $p$ is the amplification efficiency, determine the amplification efficiency $p$ when the quantity of a DNA sample increases by a factor of $100$ after $6$ amplification cycles.

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