
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
The eccentricity of the curve $\begin{cases}x=a\sec α \\\\ y=b\tan α\\end{cases}(α\\text{ is the parameter }\\)$ and the curve $\begin{cases}x=a\tan β \\\\ y=b\sec β\\end{cases}(β\\text{ is the parameter }\\)$ are $e_{1}$ and $e_{2}$ respectively. Find the minimum value of $e_{1}+e_{2}$.

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