
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
The number 3003 is the only number known to appear eight times in Pascal's triangle, at positions
$$
\binom{3003}{1},\binom{3003}{3002},\binom{a}{2},\binom{a}{a-2},\binom{15}{b},\binom{15}{15-b},\binom{14}{6},\binom{14}{8}.
$$

Compute \( a + b(15-b) \).

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