
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
Evaluate the following expression: 
\[ \frac{a+3}{a+2} \cdot \frac{b+5}{b-3} \cdot \frac{c + 10}{c+7}, \]
given that $c = 2b - 30$, $b = 2a - 1$, $a = 6$, and ensure none of the denominators are zero.

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