
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 a sequence $\{a_n\}$ where $a_1=1$ and $a_{n+1}=a_n+2n+1$, and another sequence $\{b_n\}$ satisfies $b_n=a_n-1$. For any positive integer $n$, the inequality $\frac{1}{{b_1}}+ \frac{1}{{b_2}}+...+ \frac{1}{{b_n}} < m$ always holds. The range of the real number $m$ is ______.

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