
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 a plane Cartesian coordinate system, the parametric equations of line $l$ are given by:
$$
\begin{cases}
x = -1 + \frac{\sqrt{2}}{2}t \\
y = \frac{\sqrt{2}}{2}t
\end{cases}
$$
where $t$ is the parameter. Now, setting up a polar coordinate system with the origin as the pole and the non-negative half of the $x$-axis as the polar axis, the polar equation of curve $C$ is $\rho = 6 \cos \theta$.

(Ⅰ) Write down the standard equation of line $l$ and the Cartesian equation of curve $C$.

(Ⅱ) If point $P$ has coordinates $(-1,0)$ and line $l$ intersects curve $C$ at points $A$ and $B$, find the value of $|PA| + |PB|$.

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