
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
If $a, b$ are positive constants, $a \neq b$, and $x, y \in (0, +\infty)$, then $\frac{1}{x} + \frac{1}{y} \geq \frac{4}{x+y}$, with equality if and only if $x = y$. Using this conclusion, the minimum value of the function $f(x) = \frac{1}{1-2x} + \frac{1}{2-3x}$ can be obtained as \_\_\_\_\_\_\_\_.

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