
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 numbers \(a\) and \(b\) such that \(a + b = 1\), find the minimum value of
\[ 
M = \sqrt{1 + 2a^{2}} + 2 \sqrt{\left(\frac{5}{12}\right)^{2} + b^{2}}
\]

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