
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 solid $S'$ in the set of all points $(x, y, z)$ in the first octant such that $x + 2y \leq 1$, $2x + z \leq 1$, and $y + 2z \leq 1$. Determine the volume of $S'$.

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