
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
When the polynomial \( f(x) = x^4 + a x^3 + b x^2 + c x + d \) is divided by each of \( x-4 \), \( x-3 \), \( x+3 \), and \( x+4 \), the remainder in each case is 102. Determine all values of \( x \) for which \( f(x) = 246 \).

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