
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
Consider the propositions p and q, where
p: For all $x \in \mathbb{R}$, $|x| + x \geq 0$,
q: The equation $x^2 + mx + 1 = 0$ has real roots.
(1) Write the negation of proposition p and determine the truth value of the negation;
(2) If the composite proposition "p ∧ q" is false, determine the range of the real number m.

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