
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 that the ratio of atmospheric pressure at a certain location to atmospheric pressure at sea level is $b=e^{-kh}$, and $b=\frac{1}{2}$ at location $A$ and $b=\frac{1}{3}$ at location $B$ with an altitude of $8700$ meters, calculate the absolute value of the difference in altitude between locations $A$ and $B$.

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