
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 the mean weight of the bricks in $X$ is $60$ pounds, the mean weight in $Y$ is $70$ pounds, the mean weight in the combined piles $X$ and $Y$ is $65$ pounds, and the mean weight in the combined piles $X$ and $Z$ is $67$ pounds, determine the smallest possible integer value for the mean weight in pounds of the bricks in the combined piles $Y$ and $Z$.

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