
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 a positive integer  $ n$ , for all positive integers  $ a_1, a_2, \cdots, a_n$  that satisfy  $ a_1 \equal{} 1$ ,  $ a_{i \plus{} 1} \leq a_i \plus{} 1$ , find  $ \displaystyle \sum_{i \equal{} 1}^{n} a_1a_2 \cdots a_i$ .

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