
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
Misha and Sasha left city $A$ for city $B$ on bicycles at noon. Simultaneously, Vanya left city $B$ for city $A$. All three travel at constant but different speeds. At 1 PM, Sasha was exactly halfway between Misha and Vanya, and at 1:30 PM, Vanya was halfway between Misha and Sasha. When will Misha be exactly halfway between Sasha and Vanya?

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