
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
Given positive real numbers \(a\) and \(b\) such that \(a+b=1\), find the minimum value of the function
\[ 
f(a, b) = \left(\frac{1}{a^{5}} + a^{5} - 2\right)\left(\frac{1}{b^{5}} + b^{5} - 2\right).
\]

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