
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
Given the parametric equation of line $l$ as $$\begin{cases} x=- \frac { \sqrt {2}}{2}t \\ y=a+ \frac { \sqrt {2}}{2}t\end{cases}$$ ($t$ is the parameter, $a\in\mathbb{R}$), and the polar coordinate equation of curve $C$ as $\rho\sin^2\theta=4\cos\theta$.

1. Convert the parametric equation of line $l$ and the polar coordinate equation of curve $C$ into Cartesian coordinate equations.
2. If line $l$ passes through point $(0,1)$, find the length of the line segment intercepted by curve $C$.

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