
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 rectangular coordinate system $xOy$, the parametric equation of line $l$ is $\begin{cases} x=t \\ y=2t+2 \end{cases}$ ($t$ is the parameter), and the parametric equation of curve $C$ is $\begin{cases} x=m \\ y=m^{2} \end{cases}$ ($m$ is the parameter). In the polar coordinate system where the pole coincides with the origin of the rectangular coordinate system and the polar axis coincides with the positive half of the $x$-axis, the polar equation of circle $O$ is $\rho=a$ ($a>0$).

1. Find the value of $a$ if line $l$ is tangent to circle $O$.
2. Find the value of $|AB|$ if line $l$ intersects curve $C$ at points $A$ and $B$.

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