
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 condition p: $|5x - 1| > a$ and condition q: $x^2 - \frac{3}{2}x + \frac{1}{2} > 0$, please choose an appropriate real number value for $a$, and use the given two conditions as A and B to construct the proposition: If A, then B. Make sure the constructed original proposition is true, while its converse is false, and explain why this proposition meets the requirements.

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