
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 proposition: "In a plane, vectors $\overrightarrow {OA}$ and $\overrightarrow {OB}$ form a pair of non-parallel vectors, and $|\overrightarrow {OA}|=|\overrightarrow {OB}|=1$, $\overrightarrow {OA} \perp \overrightarrow {OB}$, then for any non-zero vector $\overrightarrow {OP}$, $\overrightarrow {OP}=\lambda_{1}\overrightarrow {OA}+\lambda_{2}\overrightarrow {OB}$ ($\lambda_{1}, \lambda_{2} \in \mathbb{R}$), if point P lies on a line $l$ passing through point O (not coinciding with OA), then $\frac {\lambda_{1}}{\lambda_{2}}=k$ (a constant), and vice versa, we call line $l$ the equi-ratio line based on $\overrightarrow {OA}$ and $\overrightarrow {OB}$, where the constant $k$ is the equi-ratio of line $l$." is a true proposition, then among the following conclusions, the ones that hold are __________ (fill in the serial numbers of all true propositions).
① When $k=1$, line $l$ passes through the midpoint of segment AB;
② When $k<-1$, line $l$ intersects the extension of AB;
③ When $k=-1$, line $l$ is parallel to AB;
④ When $l_{1} \perp l_{2}$, the corresponding equi-ratios satisfy $k_{1} \cdot k_{2}=-1$;
⑤ The angle between lines $l_{1}$ and $l_{2}$ is denoted as $\theta$ ($\theta \neq \frac {\pi}{2}$) with corresponding equi-ratios $k_{1}, k_{2}$, then $\tan\theta= \frac {|k_{1}-k_{2}|}{|1+k_{1}k_{2}|}$.

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