
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 coordinate plane, construct a right triangle with legs parallel to the $x$ and $y$ axes such that the medians to the midpoints of the legs lie on the lines $y = 2x + 3$ and $y = mx + b$. If the intersection of these medians is required to coincide with the fixed point $(4, 11)$, determine the number of different possible values for the slope $m$ and the intercept $b$.

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