
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
The calculation formula for the Richter magnitude scale ($M$) is: $M=\log A-\log A\_0$, where $A$ is the maximum amplitude of the seismic wave recorded by the seismograph, and $A\_0$ is the amplitude of the standard earthquake. Suppose in an earthquake, the maximum amplitude recorded by the seismograph is $1000$, and the amplitude of the standard earthquake $A\_0$ is $0.001$, then the magnitude of this earthquake is \_\_\_\_\_\_ ; the maximum amplitude of a $9$-magnitude earthquake is \_\_\_\_\_\_ times that of a $5$-magnitude earthquake.

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