
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
Define the distance set between two point sets $S$ and $T$ as $d\left(S,T\right)=\{|PQ||P\in S,Q\in T\}$, where $|PQ|$ represents the distance between two points $P$ and $Q$. Given $k,θ∈R$, $S=\{(x,y)|y=kx+\sqrt{5}tanθ,x∈R\}$, $T=\{(x,y)|y=\sqrt{4x^2+1},x∈R\}$, $d\left(S,T\right)=\left(1,+\infty \right)$, then one possible value of $\theta$ is ______.

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