
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 $(xOy)$, if the line $l$: $\begin{cases} x=t \\ y=t-a \end{cases}$ ($t$ is a parameter) passes through the right vertex of the ellipse $C$: $\begin{cases} x=3\cos \theta \\ y=2\sin \theta \end{cases}$ ($\theta$ is a parameter), then the value of the constant $a$ is _____.

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