
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 $l$ is represented by $$\begin{cases} x=t \\ y=t-a \end{cases}$$ (where $t$ is a parameter) and passes through the right vertex of the ellipse $C$ represented by $$\begin{cases} x=3\cos\theta \\ y=2\sin\theta \end{cases}$$ (where $\theta$ is a parameter), then the value of the constant $a$ is \_\_\_\_\_\_.

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