
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
Let $p: \forall x \in (0, +\infty)$, ${x}^{2}-5x \geq -\frac{25}{4}$; Let $q$: there exists an even number that is divisible by $3$.  
$(1)$ Write the negation of $p$;  
$(2)$ Write the negation of $q$.

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