
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
Real numbers  $X_1, X_2, \dots, X_{10}$  are chosen uniformly at random from the interval  $[0,1]$ . If the expected value of  $\min(X_1,X_2,\dots, X_{10})^4$  can be expressed as a rational number  $\frac{m}{n}$  for relatively prime positive integers  $m$  and  $n$ , what is  $m+n$ ?

*2016 CCA Math Bonanza Lightning #4.4*

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