
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 parabola $C: y^2 = 4x$ with focus $F$, and a line $MN$ passing through the focus $F$ and intersecting the parabola $C$ at points $M$ and $N$. Let $D$ be a point on the line segment $MF$, and $|MD| = 2|NF|$. If $|DF| = 1$, then $|MF| = \_\_\_\_\_\_$.

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