
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
3.  Six points A, B, C, D, E, F are connected with segments length of  $1$ .  Each segment is painted red or black probability of  $\frac{1}{2}$  independence.  When point A to Point E exist through segments painted red, let  $X$  be.  Let  $X=0$  be non-exist it.  Then, for  $n=0,2,4$ , find the probability of  $X=n$ .

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