
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
Given a line $l$ with an inclination angle of $45^\circ$, its parametric equation is $$\begin{cases} x=1+mt \\ y=2+ \frac { \sqrt {2}}{2}t \end{cases}$$ (where $t$ is the parameter). In the Cartesian coordinate system $xOy$, point $P(1,2)$, with $O$ as the pole and the positive half-axis of $x$ as the polar axis, establishes a polar coordinate system. The polar equation of curve $M$ is $\rho^2(5\cos^2\theta-1)=4$. Line $l$ intersects curve $M$ at points $A$ and $B$.  
(1) Find the value of $m$ and the Cartesian equation of curve $M$;  
(2) Find the value of $|PA|\cdot|PB|$.

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