
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, the parametric equation of curve $C_{1}$ is 
$$
\begin{cases} 
x=3+ \sqrt {2}\cos \alpha \\ 
y=1+ \sqrt {2}\sin \alpha
\end{cases}
(\alpha \text{ is the parameter})
$$
With the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. In this polar coordinate system, there is a ray $l$: $\theta= \frac {\pi}{4}(\rho\geqslant 0)$ and curve $C_{2}$: $\rho(\sin \theta+2\cos \theta)=\rho^{2}\cos ^{2}\theta+m$.  
$(1)$ Determine the number of common points between ray $l$ and curve $C_{1}$;  
$(2)$ If ray $l$ intersects curve $C_{2}$ at points $A$ and $B$, and satisfies $|OA|=|AB|$, find the value of the real number $m$.

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