
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  $a$ ,  $b$ , and  $c$  be real numbers such that  $0\le a,b,c\le 5$  and  $2a + b + c = 10$ . Over all possible values of  $a$ ,  $b$ , and  $c$ , determine the maximum possible value of  $a + 2b + 3c$ .

*Proposed by Andrew Wen*

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