
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
A cube $PQRSTUWV,$ labeled as shown below, has edge length $2$ and is cut by a plane passing through vertex $P$ and the midpoints $X$ and $Y$ of $\overline{QR}$ and $\overline{TU}$ respectively. The plane divides the cube into two solids. Find the volume of the smaller of the two solids.

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