
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]


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The sum of the first three terms of an arithmetic progression, as well as the sum of the first six terms, are natural numbers. Additionally, its first term \( d_{1} \) satisfies the inequality \( d_{1} \geqslant \frac{1}{2} \). What is the smallest possible value that \( d_{1} \) can take?

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