
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 a cube $ABCD-A_1B_1C_1D_1$ with an edge length of $2$, point $O$ is the center of the base $ABCD$. A point $P$ is randomly selected inside the cube $ABCD-A_1B_1D_1$. Calculate the probability that the distance from point $P$ to point $O$ is greater than $1$.

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