
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 a geometric sequence with positive terms $\{a_n\}$, $a_2$ and $a_6$ are the two roots of the equation $3x^2 - 10x + 3 = 0$. Calculate the value of $\dfrac{1}{a_2} + \dfrac{1}{a_6} + a_4^2$.

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