
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
$\triangle ABC$ and $\triangle DEF$ share side $BC$. $AB = 7\ \text{cm}$, $AC = 15\ \text{cm}$, $DF = 10\ \text{cm}$, and $DE = 25\ \text{cm}$. What is the least possible integral number of centimeters for side $BC$?

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