
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
In the cube \( ABCD A_1 B_1 C_1 D_1 \), where \( AA_1, BB_1, CC_1 \), and \( DD_1 \) are parallel edges, a plane \( P \) passes through the point \( D \) and the midpoints of the edges \( A_1D_1 \) and \( C_1D_1 \). Find the distance from the midpoint of the edge \( AA_1 \) to the plane \( P \), given that the edge of the cube is 2.

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