
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
Let \( n = 1 + 3 + 5 + \ldots + 31 \) and \( m = 2 + 4 + 6 \ldots + 32 \). If \( a = m - n \), find the value of \( a \).

If \(ABCD\) is a trapezium, \( AB = 4 \text{ cm}, EF = a \text{ cm}, CD = 22 \text{ cm} \) and \( FD = 8 \text{ cm} \), if the area of \( ABEF \) is \( b \text{ cm}^2 \), find the value of \( b \).

In \(\triangle ABC\), \( AB = AC = 10 \text{ cm} \) and \( \angle ABC = b^\circ - 100^\circ \). If \(\triangle ABC\) has \( c \) axis of symmetry, find the value of \( c \).

Let \( d \) be the least real root of the \( cx^{\frac{2}{3}} - 8x^{\frac{1}{3}} + 4 = 0 \), find the value of \( d \).

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