
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
Given \( f(x)=\left(x^{2}+3 x+2\right)^{\cos \pi x} \), determine the sum of all \( n \) that satisfy the equation
\[ \left|\sum_{k=1}^{n} \log_{10} f(k)\right|=1 \]

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