
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
Maurice travels to work either by his own car (and then due to traffic jams, he is late in half the cases) or by subway (and then he is late only one out of four times). If on a given day Maurice arrives at work on time, he always uses the same mode of transportation the next day as he did the day before. If he is late for work, he changes his mode of transportation the next day. Given all this, how likely is it that Maurice will be late for work on his 467th trip?

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