
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 $\triangle ABC$, $AB= 300$, $BC=350$, and $AC=400$. An interior point $P$ is drawn such that segments through $P$ parallel to the sides of the triangle divide the triangle into segments of lengths $x$, $y$, and $z$. If $x+y+z = 750$, find $d$, the common difference between the segments.

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