
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
A line $l$ passes through point $P(2,1)$ with an inclination angle of $\frac{\pi}{4}$. The curve $C$ is defined by the parametric equations: $\begin{cases} x = 2\sqrt{2} \cos \theta \\ y = 2 \sin \theta \end{cases} (\theta \text{ is the parameter})$.
(1) Write the standard form of the parametric equation of line $l$ and find the general equation of curve $C$;
(2) If line $l$ intersects curve $C$ at points $A$ and $B$, find $|AB|$.

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