
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 general formulas of sequences $\{a_{n}\}$, $\{b_{n}\}$, and $\{c_{n}\}$ as ${a_n}=\frac{{40}}{n}$, ${b_n}=\frac{{80}}{s}$, ${c_n}=\frac{{60}}{t}$, where $n+s+t=200$, $s=kn$, $n$, $s$, $t$, $k\in N^{*}$. Let $M_{n}=\max \{a_{n}$, $b_{n}$, $c_{n}\}$ (where $\max \{a_{n}$, $b_{n}$, $c_{n}\}$ represents the maximum value among $a_{n}$, $b_{n}$, $c_{n}$), then for any $k\in N^{*}$, the minimum value of $M_{n}$ is ____.

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