
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 that isosceles $\triangle ABC$ has $\overline{AB} = \overline{BC} = 3$ and $\overline{AC} = 4$, $M$ is the midpoint of $\overline{AB}$, and $D$ is a point on $\overline{BC}$ such that $BD = 1$, determine the area of $\triangle BDM$.

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