
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 a quadratic function $f(x) = ax^2 + x$ has a minimum value, the solution set of the inequality $f(x) < 0$ is set $A$.
(1) Find the set $A$;
(2) Let set $B = \{x \,|\, |x+4| < a\}$, if set $B$ is a subset of set $A$, find the range of $a$.

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