
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 functions $f(x)=x^{2}+4x$ and $g(a)=|a-2|+|a+1|$,

(1) Solve the inequality: $f(x)\geq g(3)$;

(2) If there exists a real number $x$ such that the equation $f(x)+g(a)=0$ holds, find the range of values for the real number $a$.

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