
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
Find the difference between the maximum value and the minimum value of the sum $a_1 + 2a_2 + 3a_3 + 4a_4 + 5a_5$, where $\{a_1,a_2,a_3,a_4,a_5\} = \{1,2,3,4,5\}$.

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