
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
Given two numbers $a$ and $b$, a new number $c$ is generated according to the rule $c = a + b + ab$, and such a new number $c$ is called a "lucky number". Then, from the three numbers $a$, $b$, and $c$, any two numbers can be chosen, and according to the rule, another "lucky number" can be generated. Each generation of a "lucky number" is considered one operation. Now, with the numbers 1 and 4, and operating according to the above rule three times, the largest "lucky number" obtained is.

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