
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
Inside a right triangle \(ABC\) with hypotenuse \(AC\), a point \(M\) is chosen such that the areas of triangles \(ABM\) and \(BCM\) are one-third and one-quarter of the area of triangle \(ABC\) respectively. Find \(BM\) if \(AM = 60\) and \(CM = 70\). If the answer is not an integer, round it to the nearest whole number.

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