
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 \( g(x) = ax^2 + bx + c \) where \( a \), \( b \), and \( c \) are integers. Suppose that \( g(2) = 0 \), \( 60 < g(6) < 70 \), \( 80 < g(9) < 90 \), and \( 6000l < g(100) < 6000(l+1) \) for some integer \( l \). What is \( l \)?

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