
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 $f(x) = |x-3| + |x-4|$.

(1) If the solution set of the inequality $f(x) < a$ with respect to $x$ is not empty, find the range of values for the real number $a$;

(2) Solve the inequality: $f(x) \geqslant 7 + 7x - x^2$.

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