
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
Let $a$ and $b$ be two distinct real roots of the equation $t^{2}\cos θ+t\sin θ=0$ with respect to $t$. The number of common points between the line passing through $A(a,a^{2})$ and $B(b,b^{2})$ and the hyperbola $\frac {x^{2}}{\cos ^{2}θ}- \frac {y^{2}}{\sin ^{2}θ}=1$ is _______ .

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