
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 \( a \) and \( b \) be real numbers such that \( a + b = 1 \). Then, the minimum value of 
\[ 
f(a, b) = 3 \sqrt{1 + 2a^2} + 2 \sqrt{40 + 9b^2} 
\] 
is ______.

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