
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
Among the following four propositions, the false one is \_\_\_\_\_\_ (fill in the serial number).

① A line passing through a fixed point $P(x_{0},y_{0})$ cannot always be represented by the equation $y-y_{0}=k(x-x_{0})$;

② A line passing through two different points $P_{1}(x_{1},y_{1})$, $P_{2}(x_{2},y_{2})$ can always be represented by the equation $(y-y_{1})(x_{2}-x_{1})=(x-x_{1})(y_{2}-y_{1})$;

③ A line that intersects both coordinate axes cannot always be represented by the equation $\dfrac{x}{a}+ \dfrac{y}{b}=1$;

④ A line passing through point $Q(0,b)$ can always be represented as $y=kx+b$.

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