
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 Cartesian coordinate system $xOy$, it is known that curve $C_{1}$: $\begin{cases} & x=t+1 \\ & y=1-2t \end{cases}$ (where $t$ is a parameter) and curve $C_{2}$: $\begin{cases} & x=a\sin \theta \\ & y=3\cos \theta \end{cases}$ (where $\theta$ is a parameter, $a > 0$) have one common point on the $x$-axis. Find the value of $a$.

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