
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 proposition p: The graph of the equation $$\frac {x^{2}}{4-m}+ \frac {y^{2}}{m}=1$$ is an ellipse with foci on the x-axis; proposition q: "For all $x \in \mathbb{R}, x^2+2mx+1>0$"; proposition S: "There exists $x \in \mathbb{R}, mx^2+2mx+2-m=0$."
(1) If proposition S is true, find the range of the real number $m$;
(2) If $p \lor q$ is true, and $\lnot q$ is true, find the range of the real number $m$.

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