
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 functions $f(x)=|x+1|+|x-3|$ and $g(x)=a-|x-2|$.
1. Find the range of values for the real number $a$ such that the inequality $f(x) < g(x)$ has a solution in terms of $x$.
2. If the solution set of the inequality $f(x) < g(x)$ is $(b, \frac{7}{2})$, find the value of $a+b$.

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