
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 that $m,n\in {{R}^{+}},m\neq n,x,y\in (0,+\infty )$, it follows that $\dfrac{{{m}^{2}}}{x}+\dfrac{{{n}^{2}}}{y}\geqslant \dfrac{{{(m+n)}^{2}}}{x+y}$, with equality holding when $\dfrac{m}{x}=\dfrac{n}{y}$. Utilize this conclusion to determine the minimum value of the function $f(x)=\dfrac{4}{3x}+\dfrac{3}{1-x}$, where $x\in (0,1)$.

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