
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 symbols for two operations. Initially, the display shows the number 0. You can press any keys in any sequence. The calculator performs actions in the order of key presses. If an operation symbol is pressed consecutively, the calculator remembers only the last press. The Scatterbrained Scientist pressed a lot of buttons in random order. 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}
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