
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
In the geometric sequence $\{{{a}_{n}}\}$, if ${{a}_{n}} > 0$ and ${{a}_{7}}=\dfrac{\sqrt{2}}{2}$, find the minimum value of $\dfrac{1}{{{a}_{3}}}+\dfrac{2}{{{a}_{11}}}$.

A) $4$
B) $8$
C) $2\sqrt{2}$
D) $16$

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