
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
Let \( d_1 = x^2 + 3^x + x \cdot 3^{(x+1)/2} \) and \( d_2 = x^2 + 3^x - x \cdot 3^{(x+1)/2} \). If \( 1 \le x \le 301 \), how many integral values of \( x \) are there such that \( d_1 \cdot d_2 \) is a multiple of \( 7 \)?

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