
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 triangle shown below, for $\angle B$ to be the largest angle of the triangle, the relationship between $x$ must be defined. Side lengths of the triangle are given by $BC = x + 12$, $AB = 2x + 3$, and $AC = 4x - 5$. Determine the possible range for $x$ such that these conditions are satisfied. 
[asy]
 draw((0,0)--(2,0)--(1,1.5)--cycle);
 label("$B$",(1,1.5),N); label("$C$",(2,0),SE); label("$A$",(0,0),SW);
 label("$x+12$",(1.5,0.75),NE); label("$2x+3$",(0.5,0.75),NW); label("$4x-5$",(1,-0.2),S);
[/asy]

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