
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 $y=a\sin x+b\cos x+c$ has a lowest point $(\frac{11π}{6},1)$ on its graph. If the ordinate of each point on the graph remains unchanged, the abscissa is shortened to $\frac{3}{π}$ of the original, and then shifted to the left by 1 unit length to obtain the graph of $y=f\left(x\right)$, and all roots of $f\left(x\right)=3$ differ by 3 units in increasing order, then $a+b+c=\_\_\_\_\_\_$.

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