
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 cube \(ABCD A_1 B_1 C_1 D_1\), where \(A A_1\), \(B B_1\), \(C C_1\), and \(D D_1\) are parallel edges, plane \(P\) passes through point \(D\) and the midpoints of edges \(A_1 D_1\) and \(C_1 D_1\). Find the distance from the midpoint of edge \(A A_1\) to plane \(P\), given that the edge length of the cube is 2.

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