
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 the sequence ${a_n}$ is an arithmetic sequence, with $a_1 \geq 1$, $a_2 \leq 5$, $a_5 \geq 8$, let the sum of the first n terms of the sequence be $S_n$. The maximum value of $S_{15}$ is $M$, and the minimum value is $m$. Determine $M+m$.

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