
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
Consider the sequence of six real numbers 60, 10, 100, 150, 30, and  $x$ .  The average (arithmetic mean) of this sequence is equal to the median of the sequence.  What is the sum of all the possible values of  $x$ ?  (The median of a sequence of six real numbers is the average of the two middle numbers after all the numbers have been arranged in increasing order.)

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