
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 triangle $\mathrm{ABC}$, point $\mathrm{M}$ is the midpoint of $\mathrm{AC}$. $\mathrm{MD}$ and $\mathrm{ME}$ are bisectors of triangles $\mathrm{ABM}$ and $\mathrm{CBM}$, respectively. Segments $\mathrm{BM}$ and $\mathrm{DE}$ intersect at point $\mathrm{F}$. Find $\mathrm{MF}$ if $\mathrm{DE}=7$.

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