
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 a cube ABCD-A<sub>1</sub>B<sub>1</sub>C<sub>1</sub>D<sub>1</sub> with edge length 1, F is the midpoint of edge BC, and M is a moving point on the line segment A<sub>1</sub>F. The minimum value of the sum of the areas of △MDD<sub>1</sub> and △MCC<sub>1</sub> is \_\_\_\_\_\_.

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