
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 $xOy$, with the origin as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. It is known that the polar coordinates of curve $C$ are $\rho =2\cos \theta$, and the line $l: \begin{cases} & x=m+3t \\ & y=4t \end{cases}$ (where $t$ is a parameter) intersects curve $C$ at two distinct points $A$ and $B$.

$(1)$ Find the range of values for the real number $m$;

$(2)$ Let point $M(m,0)$. If $|MA| \cdot |MB|=1$, find the value of the real number $m$.

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