
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 sequence of numbers $a_1, a_2, \ldots, a_n$ that satisfies the relation: each subsequent number is greater than the previous one by a constant value $k$, and $3(a_3 + a_5) + 2(a_7 + a_{10} + a_{13}) = 24$, find the value of $a_1 + a_2 + \ldots + a_{13}$.

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