
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 that F is the focus of the curve defined by the parametric equations $$\begin{cases} x=2\cos\theta \\ y=1+\cos2\theta \end{cases}$$ ($\theta\in\mathbb{R}$), and $M\left( \frac{1}{2},0 \right)$, find the value of $|MF|$.

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