
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 conclusion "For $a_1, a_2 \in \mathbb{R}^+$, and $a_1 + a_2 = 1$, then $\frac{1}{a_1} + \frac{1}{a_2} \geq 4$. If $a_1, a_2, a_3 \in \mathbb{R}^+$, and $a_1 + a_2 + a_3 = 1$, then $\frac{1}{a_1} + \frac{1}{a_2} + \frac{1}{a_3} \geq 9$", please conjecture that if $a_1, a_2, \ldots, a_n \in \mathbb{R}^+$, and $a_1 + a_2 + \ldots + a_n = 1$, then $\frac{1}{a_1} + \frac{1}{a_2} + \ldots + \frac{1}{a_n} \geq$ ______.

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