
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
Let $A \Delta B = AB + A + B$, such as $2 \Delta 3 = 2 \times 3 + 2 + 3 = 11$, then $( (1 \Delta 9) \Delta 9 ) \Delta 9 = \ $? And $((1 \Delta 9) \Delta 9) \Delta 9 \ldots ) \Delta 9$ (with a total of $n$ nines) $= \ $? ($n$ is a positive integer).

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