
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
(This question is worth 10 points) Elective 4-5: Inequality Selection

Let there be an inequality regarding $x$: $\lg(|x+3|+|x-7|) > a$.

(1) Solve this inequality when $a=1$;

(2) For what value of $a$ does the solution set of this inequality become $\mathbb{R}$.

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