
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
On the diagonals \(AC\) and \(BD\) of the trapezoid \(ABCD\), points \(M\) and \(N\) are taken respectively such that \(AM : MC = DN : NB = 1 : 4\). Find \(MN\), if the bases \(AD = a\) and \(BC = b\) with \(a > b\).

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