
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, the parametric equation of curve \( C \) is given by \(\begin{cases}x= \sqrt{5}\cos \alpha \\ y=\sin \alpha\end{cases} (\alpha\) is the parameter)\().\) A polar coordinate system is established with the origin \( O \) as the pole and the positive \( x \)-axis as the initial line. The polar equation of line \( l \) is \( \rho\cos (\theta+ \frac {\pi}{4})= \sqrt {2} \). Line \( l \) intersects curve \( C \) at points \( A \) and \( B \).
(Ⅰ) Find the standard equation of curve \( C \) and the Cartesian equation of line \( l \);
(Ⅱ) Let \( P(0,-2) \) be a point on the plane, find the value of \( |PA|+|PB| \).

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