
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
The base  $5$  number  $32$  is equal to the base  $7$  number  $23$ . There are two  $3$ -digit numbers in base  $5$  which similarly have their digits reversed when expressed in base  $7$ . What is their sum, in base  $5$ ? (You do not need to include the base  $5$  subscript in your answer).

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