
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
A calculator has digits from 0 to 9 and signs of two operations. Initially, the display shows the number 0. You can press any keys. The calculator performs operations in the sequence of keystrokes. If an operation sign is pressed several times in a row, the calculator remembers only the last press. A distracted Scientist pressed many buttons in a random sequence. Find approximately the probability that the result of the resulting sequence of actions is an odd number?

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