
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
To climb from the valley to the top of the mountain, you need to travel for 6 hours on a road and then for 6 hours on a path. At the top of the mountain live two fire-breathing dragons. The first dragon breathes fire for 1 hour, then sleeps for 25 hours, then breathes fire again for 1 hour, and so on. The second dragon breathes fire for 1 hour, then sleeps for 13 hours, then breathes fire again for 1 hour, and so on. When the first dragon is breathing fire, it is dangerous to travel on both the road and the path. When the second dragon is breathing fire, it is dangerous to travel only on the path. Both dragons start breathing fire simultaneously at midnight. Is it possible to safely climb from the valley to the top of the mountain and return?

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