
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
From Picklminster to Quickville. Two trains $A$ and $B$ depart from Picklminster to Quickville simultaneously with trains $C$ and $D$, which depart from Quickville to Picklminster. Train $A$ meets train $C$ at 120 miles and train $D$ at 140 miles from Picklminster. Train $B$ meets train $C$ at 126 miles from Quickville and train $D$ halfway between Picklminster and Quickville. What is the distance from Picklminster to Quickville? All trains travel at constant speeds, not significantly different from usual.

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