
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 Oxy, it is known that curve $C_1$ with the equation $\begin{cases} x=t+1 \\ y=1-2t \end{cases}$ (t as a parameter) shares a common point with curve $C_2$ with the equation $\begin{cases} x=a\sin\theta \\ y=3\cos\theta \end{cases}$ (θ as a parameter, a>0) on the X-axis. Determine the value of $a$.

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