
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
For an integer \( n \geq 2 \) and non-negative real numbers \( a_1, a_2, \ldots, a_n \) satisfying \( \sum_{i=1}^{n} a_i = 4 \), find the maximum possible value of \( 2a_1 + a_1a_2 + a_1a_2a_3 + \ldots + a_1a_2 \ldots a_n \).

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