
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 the function $f(x) = mx^{2} + mx + 3$, where $m \in \mathbb{R}$.  
$(1)$ If the inequality $f(x) > 0$ always holds for all real numbers $x$, find the range of real numbers for $m$.  
$(2)$ Solve the inequality $f(x) > (3m-1)x + 5$.

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