
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
On a calculator's keyboard, there are digits from 0 to 9 and signs for two operations. Initially, the display shows the number 0. You can press any keys. The calculator performs actions in the sequence of key presses. If an operation sign is pressed several times in a row, the calculator remembers only the last press. A distracted Scientist pressed a lot of buttons in a random sequence. Approximately find the probability that the result of the resulting sequence of actions is an odd number?

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