
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 a hyperbola $\dfrac {x^{2}}{4}-y^{2}=1$ and a point $P$ on it, draw two lines $l_{1}$ and $l_{2}$ parallel to the asymptotes of the hyperbola passing through the point $P$. If lines $l_{1}$ and $l_{2}$ intersect the $x$-axis at points $M$ and $N$ respectively, then find the product $|OM|\cdot|ON|$.

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