
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 TGV departs from Paris at $150 \text{ km/h}$ toward Marseille, which is $800 \text{ km}$ away. An intercité departs from Marseille at $50 \text{ km/h}$ toward Paris at the same time. A swallow perched on the TGV takes off at that moment, flying at $200 \text{ km/h}$ toward Marseille. When it reaches the intercité, it turns around, and when it reaches the TGV, it turns around again, and so on. What distance will it have flown when the two trains meet?

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