
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
Elective 4-4: Coordinate System and Parametric Equations

In the Cartesian coordinate system $xoy$, the curve $C_{1}$ has the parametric equations $\begin{cases} & x=a\cos t \\ & y=1+a\sin t \\ \end{cases}$ (where $t$ is the parameter, $a > 0$). In the polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis, the curve $C_{2}$ is given by $\rho=4\cos \theta$.

(Ⅰ) Explain what kind of curve $C_{1}$ is and convert the equation of $C_{1}$ into a polar coordinate equation;

(Ⅱ) The polar coordinate equation of line $C_{3}$ is $\theta=a_{0}$, where $a_{0}$ satisfies $\tan a_{0}=2$. If all the common points of curves $C_{1}$ and $C_{2}$ lie on $C_{3}$, find $a$.

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