
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 two real numbers and let $M(a,b)=\max\left \{ 3a^{2}+2b; 3b^{2}+2a\right \}$ . Find the values of  $a$  and  $b$  for which  $M(a,b)$  is minimal.

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