
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 inequality $2|x-3|+|x-4| < a^{2}+a$,

(1) If $a=1$, find the solution set of the inequality;

(2) If the solution set of the inequality is not empty, and $a$ is a positive integer, find the smallest integer value of $a$ that satisfies the condition.

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