
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 \( a, b, c, d \in \mathbb{R} \) such that \( a + 3b + 5c + 7d = 14 \). Find the minimum possible value of \( a^{2} + b^{2} + c^{2} + d^{2} \).

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