
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 sequence $\{a\_n\}$ satisfies $a\_n - a_{n+1} = a\_n a_{n+1} (n \in \mathbb{N}^*)$, and the sequence $\{b\_n\}$ satisfies $b\_n = \frac{1}{a\_n}$, determine the maximum value of $b\_4 \cdot b\_6$.

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