
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 parallelogram $ABCD$ has sides $AB = 153 \ \text{cm}$, $AD = 180 \ \text{cm}$, and height $BE = 135 \ \text{cm}$ (where $BE$ is the height from $B$ to $AD$). This parallelogram is divided into three equal areas by lines perpendicular to $AD$. At what distances from point $A$ are the points where these perpendicular lines intersect $AD$?

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