
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
How many ordered triples of integers \( (a, b, c) \), with \( a \geq 3 \), \( b \geq 2 \), and \( c \geq 1 \), satisfy both \(\log_a b = c^2\) and \( a + b + c = 2010\)?
A) 0 
B) 1 
C) 2 
D) 3 
E) 4

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