
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
Point \( M \) divides side \( BC \) of triangle \( ABC \) in the ratio \( BM: MC = 2:5 \). Given that \( \overrightarrow{AB} = \vec{a} \) and \( \overrightarrow{AC} = \vec{b} \), find the vector \( \overrightarrow{AM} \).

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