
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 $X$, $Y$, and $Z$ are pairwise disjoint sets of people with the average ages of people in the sets $X$, $Y$, $Z$, $X \cup Y$, $X \cup Z$, and $Y \cup Z$ being $37$, $23$, $41$, $29$, $39.5$, and $33$ respectively, determine the average age of the people in the set $X \cup Y \cup Z$.

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