
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
Baba Yaga needs to arrive at Bald Mountain exactly at midnight. She calculates that if she flies in her mortar at a speed of 50 km/h, she will be 2 hours late, and if she flies on her electric broom at a speed of 150 km/h, she will arrive 2 hours early. To arrive at Bald Mountain exactly on time, Baba Yaga uses her broom. At what time did Baba Yaga depart and at what speed did she fly on the broom?

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