
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 the function $f(x)=|x+3|$, $g(x)=|2x-1|$.
$(1)$ Solve the inequality $f(x) < g(x)$;
$(2)$ If $2f(x)+g(x) > ax+4$ holds for any real number $x$, find the range of values for $a$.

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