
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  $\triangle ABC$ ,  $AB= 425$ ,  $BC=450$ , and  $AC=510$ . An interior point  $P$  is then drawn, and segments are drawn through  $P$  parallel to the sides of the triangle. If these three segments are of an equal length  $d$ , find  $d$ .

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