
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 $xoy$, the parametric equation of line $l$ is $ \begin{cases} x=1+2t\\y=2+t \end{cases} (t \text{ is the parameter })$, and in the polar coordinate system with coordinate origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the polar coordinate equation of circle $C$ is $ρ=2$.
(1) Write the general equation of line $l$ and the standard equation of circle $C$;
(2) Suppose $P(-1,1)$, and line $l$ intersects circle $C$ at points $A$ and $B$. Find the value of $|PA|-|PB|$.

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