
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 sequences $\{a_n\}$ and $\{b_n\}$ where $\frac{1}{a_{n+1}}=\frac{1}{a_n}+1$ for $n\in\mathbb{N}_+$, and $b_n=\frac{1}{a_n}$, calculate the value of $b_4b_6$ given that $b_1+b_2+\ldots+b_9=45$.

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