
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
There is a calculator with digits from 0 to 9 and two operation symbols. Initially, the display shows the number 0. You can press any buttons. The calculator performs actions in the sequence of button presses. If an operation symbol is pressed multiple times in a row, the calculator only remembers the last press. A scattered scientist pressed a lot of buttons in a random sequence. Estimate the probability that the result of the resulting chain of operations is an odd number.

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