
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 plane rectangular coordinate system $xOy$, the parametric equations of the line $l$ are $\left\{{\begin{array}{l}{x=2+\sqrt{2}t}\\{y=2+\sqrt{2}t}\end{array}}\right.$ (where $t$ is a parameter), the parametric equations of curve $C_{1}$ are $\left\{{\begin{array}{l}{x=2+\sqrt{2}\cos\alpha}\\{y=\sqrt{2}\sin\alpha}\end{array}}\right.$ (where $\alpha$ is a parameter), and a polar coordinate system is established with $O$ as the pole and the non-negative $x$-axis as the polar axis. The polar coordinate equation of curve $C_{2}$ is $\rho \sin^{2}\theta =4\cos\theta$. <br/>$(1)$ Find the polar coordinate equation of curve $C_{1}$; <br/>$(2)$ The line $l$ intersects curves $C_{1}$ and $C_{2}$ at points $A$ and $B$ (different from the origin). Find the value of $|AB|$.

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