
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
In the rectangular coordinate system $(xOy)$, the curve $C\_1: \begin{cases} x=t+ \frac {1}{t} \\ y=t- \frac {1}{t}\end{cases}(t)$ is given as a parameter, and the curve $C\_2: \begin{cases} x=a\cos \theta \\ y=\sin \theta \end{cases}(\theta)$ is given as a parameter, where $a > 1$. If $C\_1$ passes through the focus of $C\_2$, then the value of $a$ is $\_\_\_\_\_\_$.

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