
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
Determine the cube, given the following 7 points:

- $A_1$ and $A_2$: points on the plane of the lower face,
- $F_1$ and $F_2$: points on the plane of the upper face (the 4 points are not coplanar),
- $E$: a point on the plane of the front face,
- $H$: a point on the plane of the back face,
- $J$: a point on the plane of the right face.

What is the maximum number of such cubes?

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