
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
In the arithmetic sequence $\{a_n\}$, where $(a_1 > 0, a_{10} \cdot a_{11} < 0)$, the sum of the first 10 terms is $S_{10} = 36$, and the sum of the first 18 terms is $S_{18} = 12$. Find the value of $T_{18}$, the sum of the first 18 terms of the sequence $\{|a_n|\}$.

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