
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
If $\log_{10} (3x^2 - 5x + k) = 2$, and knowing that $2x + 5 = k$, find the possible values of $x$.
**A)** $\frac{38}{6}$ and $\frac{-32}{6}$  
**B)** $\frac{36}{6}$ and $\frac{-30}{6}$  
**C)** $\frac{37}{7}$ and $\frac{-31}{7}$  
**D)** $\frac{37}{6}$ and $\frac{-31}{6}$  
**E)** None of the above

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