
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 plane rectangular coordinate system $xOy$, if the line $l: \left\{\begin{array}{l}x=t\\ y=t-a\end{array}\right.$ (where $t$ is a parameter) passes through the right vertex of the ellipse $C: \left\{\begin{array}{l}x=3\cos\varphi\\ y=2\sin\varphi\end{array}\right.$ (where $\varphi$ is a parameter), then the value of the constant $a$ is ____.

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