
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
Execute the following program:  
```
INPUT  a  
i=1  
DO  
a=2*a-1  
i=i+1  
LOOP UNTIL i>10  
PRINT a|END
```  
If the input value of $a$ is from the first ten positive integers, then the probability that the output value of $a$ belongs to $\{1, 1025, 2252, 3049\}$ is.

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