
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
Triangle $ABC$ is an isosceles triangle with $AB=BC$. Point $D$ is the midpoint of both $\overline{BC}$ and $\overline{AE}$, while point $F$ is the midpoint of $\overline{AC}$. If $\overline{CE}$ is 15 units long, determine the length of $\overline{BD}$. Express your answer as a decimal to the nearest tenth.
[asy]
draw((0,0)--(3,112^.5)--(6,0)--cycle);
draw((6,0)--(9,112^.5)--(0,0));
label("$A$", (0,0), SW);
label("$B$", (3,112^.5), N);
label("$C$", (6,0), SE);
label("$D$", (4.75,6), N);
label("$E$", (9,112^.5), N);
label("$F$", (1.5,112^.5/2), NW);
[/asy]

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