
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

Detective Bashkovitsky discovered that the key witness is the one from the Petrovs' family who came home first on the fateful day. The investigation revealed the following facts:

1. Neighbor Maria Kuzminichnaya wanted to borrow some salt from the Petrovs and rang their doorbell, but no one answered. When did this happen? Who knows? It was already dark...
2. Galina Efimovna Petrova, coming home in the evening, found both children in the kitchen and her husband on the couch with a headache.
3. Husband Anatoly Ivanovich claimed that as soon as he came home, he lay down on the couch and dozed off, seeing no one, hearing nothing, and the neighbor definitely didn't come by because the doorbell would have woken him.
4. Daughter Svetlana said that upon returning home, she went straight to her room, knowing nothing about her father but as usual, tripped over Dima's shoe in the hallway.
5. Dmitry doesn't remember when he came home, he didn't see his father, but he did hear Svetka cursing about the shoe.

What is the probability that Dmitry returned home before his father?

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