
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 function $f(x) = \sin^2(ωx) - \frac{1}{2}$ $(ω > 0)$ has a minimum positive period of $\frac{π}{2}$, determine the minimum value of the real number $a$ for which the graph of $f(x)$ translated to the right by $a$ units along the $x$-axis and symmetric about the origin.

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