
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
An equilateral triangle with side length 10 is divided into 100 smaller equilateral triangles, each with side length 1, by lines parallel to its sides. There are \( m \) equilateral tiles, each composed of 4 unit triangles, and \( 25 - m \) straight tiles, each also composed of 4 unit triangles. For which values of \( m \) can these tiles be used to tile the original triangle? [Note: The straight tiles may be turned over.]

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