
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
In the given right-angled triangle $ABC$, with the angle at $B$ being a right angle (90 degrees), $D$ is a point on $BC$. The ratio of $BD$ to $DC$ is $5$ to $2$. The area of $\triangle ABD$ is given as $35$ square centimeters. Calculate the area of $\triangle ADC$.
[asy] size(85); defaultpen(linewidth(1)+fontsize(10));

pair A = (0,5.5), B=(0,0), D = (3.5,0), C = (5,0);

draw(A--B--C--A--D); label("A",A,N); label("B",B,S); label("C",C,S); label("D",D,S);
draw(rightanglemark(A,B,C,8),linewidth(0.7));
[/asy]

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