
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 \( a, b, c, d, e, f \) be positive real numbers such that \( a + b + c + d + e + f = 10 \). Find the minimum value of
\[
\frac{1}{a} + \frac{1}{b} + \frac{4}{c} + \frac{9}{d} + \frac{16}{e} + \frac{25}{f}.
\]

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